Configuration...
If this is your only sink, then I suggest a large 2-bowl sink with one large bowl and one smallish bowl.
For example, a sink that fits in a 36" to 38" sink base cabinet that has a large bowl at least 20" wide (left-to-right) and a smaller bowl at least 10" wide.
This allows you to have a bowl for cleanup and a bowl for prepping. The larger bowl is generally big enough to fit most shelves in a refrigerator and most pots/pans/cookie sheets.
It also allows you to have something soaking in one sink while you use the others sink.What I do not recommend is a two-bowl sink with equal-sized bowls - unless it is a very large sink! Maybe 45" wide or more. Equal-sized bowls in 36" (+/-) or less sink base cabinets are too small for many tasks and too big for others. You have more options and flexibility with a large + small bowl.
A compromise that some people do is get a "low divide" sink. This is a 2-bowl sink, but the divider is only about half the depth of the sink - it's a "low" divider. It gives you the flexibility of a 2-bowl sink while giving you some help with the larger items b/c you can balance them on the divider and utilize both sides or the handle of a pot can extend over the divider.
OTOH (on the other hand), if you will have two sinks in your kitchen (a prep sink in the primary Prep Zone and another sink in the Cleanup Zone - preferably separated), then my recommendation changes - I would go for a single-bowl prep sink at least 15" to 17" wide (even wider, if you have the room!) and a single-bowl cleanup sink 30" or so wide (fitting in a 33" wide sink base cabinet).
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Mounting...
Undermount...Generally the best looking type of mounting is undermounting. This is where the sink is mounted b/w the cabinets and the countertop and it is installed at the same time as the counters. It's much easier to clean the counters (sweep the crumbs into the sink) and there's no rim for "gunk" to get stuck in. This type of mounting works well for natural stone (granite, marble, etc.) and engineered stone (engineered quartz like Silestone, Cambria, etc.).
With laminate and wood, careful thought and consideration are needed to undermount a sink. Yes, it can be done, but it needs to be done right and I do not recommend someone with only basic DIY skills attempt it!
Top/overmount...this is the easiest to install and used to be the norm many years ago. However, over time and with the current general preference for natural or engineered stone for counters, it is becoming less and less used. This is where the sink is mounted on top of the counter and is installed after the counters are installed. It usually also has a deck of the same material as the rest of the sink behind the sink bowl(s) that the faucet and other fixtures are mounted on. This is usually the type of installation with laminate or wood counters. The negatives of this are that when cleaning, you have to work your way around the sink itself and crumbs, etc., can get caught b/w the counter and the sink along the sink rim. It is also more "obvious" in the overall look of the Kitchen. It's probably the easiest sink to replace, if needed/wanted.
Recessed...This is not seen much, but it's where a rim is routed in the counter in which the sink is then placed in the recessed rim. The sink is flush with the counter - so neither under nor top mount. When cleaning, you can sweep crumbs, etc., into the sink, but those crumbs will likely get caught in the groove b/w the sink and counter - no matter how tight it is! (Of course, the tighter the fit, the less crumbs will get caught, but some will inevitably get caught.)
Farm/Apron sink...This is popular in more traditional or farm/country styled kitchens but can also fit in a transitional or modern kitchen with the right materials. This is the type of sink that extends out from the cabinet - you can see the whole front of the sink.
Integrated...Solid surfaces (e.g,, Corian) have an integrated sink - it's all one piece with the counters. This is probably the easiest to keep clean. However, you cannot easily replace just the sink.
There are other, less common types as well.
Reveal (positive/zero/negative)...
When undermounting a sink, you will have the option of one of three reveals. There are pros & cons for each type of reveal:
Positive Reveal...The sink shows; granite cutout is slightly larger than sink
Pros: Easier to clean b/c you can see the gunk and can easily wipe it off (it only gets nasty if you leave it there)
Cons: Silicone (caulk?) is visible, but if they use clear you won't see it when it dries
Negative Reveal...The granite overhangs the sink; granite cutout is slightly smaller than the sink
Pros: You cannot see the gunk buildup or silicone
Cons:
You cannot see the gunk to clean it.
Dirty water/food can splash up & under where you cannot see to clean it. It's difficult to see underneath w/o leaning way over & into the sink.
Dishes/glasses have been known to break b/c when you lift them out near the edge of the sink the dish hits the stone counter & can break (or, if the dish wins, the counter could chip...but I'm not sure how likely that is).
Zero Reveal or Flush...Sink & granite are flush or even; the granite cutout & sink are the same size
Pros:
Easier to clean b/c you can see the gunk
No platform over or under for the gunk to collect
Cons:
More difficult to do perfectly
Silicone is visible, but if they use clear you won't see it when it dries
Warning: Many fabricators will use a negative reveal if you don't specifically ask for a positive or zero reveal (and won't tell you your options), or will charge you more for a non-negative reveal. This is b/c they don't have to be as careful about the sink cutout with a negative reveal - the counter extends out over the sink so any deviations in a smooth cutout following the sink contours will be hidden. (IMHO (in my humble opinion), it's lack of skill, carelessness, or laziness.)
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Depth (how deep it is/top-to-bottom)...
A deeper sink will hide dirty dishes when either the DW is full of clean dishes or full of dirty dishes. Most of us recommend a deep sink - 10" or so overall. Why do I say "overall"? Because the overall depth will depend on two things: The depth of the sink and the type of mounting.
For a top mount sink or farm/apron sink, the depth is basically the depth of the sink.
For an undermount sink, the depth is the depth of the sink + the thickness of your countertop
For a recessed sink, the depth is the depth of your sink + the amount the sink is below the counter surface (it should be zero inches, but it might be a fraction of an inch or so)
One caveat about deep sinks...the taller you are, the more difficult it is to use a deep sink. Yes, this is one of the times where shorter people have the advantage! The taller you are, the farther you have to lean down to reach the bottom - and that can be an issue for some people.
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Shape...
There are two main shapes available - "D" (with curve at top) and rectangular
The advantage of a "D" shape is that these sinks are often longer front-to-back than rectangular. This is b/c you don't need to mount faucets, etc. behind the sink - you can mount them along the sides on the curve. This is especially useful when the sink is in front of a window with a sill or on an island or peninsula with a raised counter behind it. In these situations, the window sill, counter edge, or even the backsplash of any sink facing a "wall", can often take away from the space available for the faucet and cause issues w/the faucet swiveling or the handles moving freely w/o hitting the obstruction (sill, counter edge, etc.) behind the sink.
While rectangular sinks appear to have more space b/c the full width is the same length, in reality, the "D" shapes have more b/c they have the same width up to the length of what a rectangular sink would have plus the deeper part in the curve.
The curve is exaggerated a little (it's not usually that big), but you should be able to see what I mean. In reality the "D" sink is probably only 2 or 3 inches longer top-to-bottom, but with a smaller sink, those inches can be important!
Rectangular sinks can be "zero radius" (sharp corners) or a rounded radius/corner. Some have said zero radius sinks are harder to clean in the corners - I haven't used one, but it makes sense since it would be harder to get into a sharp corner than a rounded corner.
Rectangular sinks are usually more traditional and more urban. Zero radius would fit with an urban style while a rounded radius/corners would fit with a more traditional style. I think "D" shapes fit better in a transitional kitchen - not too urban and not too traditional. This is my personal opinion. YMMV (your mileage may vary).
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How far back should it be mounted?
To reduce back strain, it's recommended the front of the sink interior be no more than 3" from the counter edge. The farther back it's mounted, the farther you have to reach to get to the faucet and other fixtures. One trick you can use to reduce that distance if you have a "D" shaped sink is to mount the faucet on the side and a bit closer to the counter edge than the top of the sink.
Note that farm and apron sinks have not front ledge, so they can be the easiest when it comes to reaching things on the bottom of the sink and, sometimes, behind the sink.
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Materials...
This has been discussed above and below my post; but to summarize/add:
Stainless Steel...Stainless steel is usually the most affordable. Note that the lower the gauge number, the thicker the sink (e.g., 16 is better than 18). SS is heat resistant, so you don't have to worry about putting a hot pot in a SS sink. Look for SS sinks with sound muffling padding on the bottom & sides (exterior) of the bowls. A brushed or satin finish hides the patina of scratches and hides most water spots. Even with polished, over time an even patina will develop and will look like it was meant to be that way. If you really hate the scratches (give it time), you can refinish the surface. [Water spots...it's a sink, you expect water in a sink!]
Solid Surface...Solid surfaces can be refinished to some extent - you can "polish" out stains and nicks and scratches. Solid surfaces will melt, so be careful about putting a pot that's too hot in the sink (or the counter). It isn't as popular as it used to be, but it may be making a comeback...
Fireclay...Many fireclay sinks are handmade (I think all Franke fireclay sinks are). Fireclay is heat resistant, so you don't have to worry about putting a hot pot in a fireclay sink. However, they are prone to cracking and chipping. They are also on the expensive side.
Porcelain (over cast iron or steel)...Porcelain sinks are prone to chipping and if the surface color is different than the material color, the chips show (personal experience here!) They are also more likely to stain (if it's a light color) than SS or granite composite sinks. Porcelain is heat resistant, so you don't have to worry about putting a hot pot in a po sink.
Granite composites...Granite composites (e.g., Silgranit) are a composite of 80% granite and 20% "other" materials (I can't seem to track down what those "other" materials are...plastic? something else? does anyone know?) If they scratch, they cannot be refinished. These sinks are usually more expensive, but many feel it's worth it.
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This is Taj with truffle
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