As an introductory note, posters here at Houzz tend to be passionate about sinks including what defines quality, sink materials that are best, and brands of sinks. Some of the most discouraging threads in which I have been involved contain comments from posters who are firm in one opinion or another and who decline to consult recommended research-based resources behind metal alloys, brand performance, and other elements involved in a sink decision while continuing to engage in back-and-forth statements. So, I'll leave the information with you, as follows, that I've gathered from research for my own sink and let you be the final judge. Whatever I or anyone else posts in response here, I recommend that you search for as many outside sources of information as you can to back up your decision about the elements of a sink that are a priority for your situation, including from scientific articles, recent reviews of a brand, and information from individual manufacturers.
Moving on to respond to your question, a quality sink on a low budget is somewhat of a challenge. You want to be looking for companies that transparently state their source of metal, whether that be recycled stainless steel or not (non-recycled is usually less prone to corrosion) and preferably 316 marine grade which is more resilient to salt-based materials (salt, brine, bleach) that can corrode stainless steel than the more commonly available 304 grade. I've seen some pros here at Houzz try to assure people that any type of stainless steel sink cannot corrode, which is untrue. The percentages of metals in the alloys that make up various grades of stainless steel govern performance on site. Chromium is the component that helps prevent corrosion in both 316 and 304 stainless steel, but 316 has molybdenum added that makes it a great choice for kitchens to resist salty compounds that may come into contact with the sink. If you can find a sink made of 316 stainless steel in non-recycled metal, then you are on your way to a quality sink. The lesser quality sinks will also be made of thinner stainless steel and may have noise issues unless they contain noise suppression padding. Better quality sinks made of preferably 16 gauge stainless steel are hefty enough on their own to usually not require padding. With any stainless steel sink, you will want to work toward keeping it dried out between uses, and you can even purchase stainless steel surface treatment products to help coat and preserve the finish if you so desire.
Let's talk now about farmhouse style stainless steel sinks. They are not as plentiful in today's market as the regular non-apron-front styles of stainless steel sinks based on my own recent shopping experience, but of course you still have a wide array of options if you can be a little flexible with your budget. If you are looking at a workstation-style sink where you can rest a cutting board and other accessories inside the sink, this also holds true as far as the non-apron-front options having the greater market share. The apron-front styles will also generally cost more just because more metal is required to make them, and this is most evident when comparing apron-front to non-apron-front options within the same brand. If cost was a huge concern over appearance or function, then the non-apron-front sink would be a way to save money. However, an apron front sink allows for a narrower lip between the user than the non-apron-front undermount, and usually sits further forward as well, so that can be a help to someone looking to prevent back strain. The beneficial ergonomics of an apron front sink was why I selected one for my own kitchen renovation.
In conclusion, one of the things you may want to consider is increasing your budget for a sink. In my own kitchen renovation, I spent months researching sinks and finally came to the realization that getting a made-to-order sink would get me everything I desired. I hadn't planned to splurge on a sink, but I made the decision to do so after my research. I went with an apron-front sink from @Havens Luxury Metals in a 42" width. My sink is a single ledge sink allowing me to put a cutting board and strainer bin inside the sink for prep and cleanup tasks. I also ordered my sink with a 3D rolled finish that Havens Metal calls "Prestige" which provides a texture that helps disguise scratches and water spots. The sink is one of my most favorite things about my renovation. If you are doing new countertops, you might consider going a little larger with your sink, up to 42", and adding some workstation accessories. However, 33" is also a nice size, just a little cramped if you want a cutting board and strainer to be utilized regularly and still have space for rinsing. Rachiele is another company that offers sinks similar to Havens Metal, and in fact, Havens Metal at one time did the production for Rachiele. Like Havens, Rachiele also offers a textured finish in stainless steel. If you wanted to re-group and go with a non-apron front style, Julien makes excellent workstation sinks in 316 stainless steel. The Galley is an expensive option that offers apron-front designs in 316 stainless steel, but I'm not a total fan of all of their accessory designs, the spotty quality of welding I observed in their Bixby, Oklahoma, showroom, or their pricing model. At the time of my sink research in 2019, The Galley charged $1,000 USD to add an apron front to its already-expensive undermount models, and they had no textured finish options. Havens Metal, in my opinion, offered the better product for my needs at a better price than The Galley, and Havens Metal was also a little better on pricing than Rachiele at the time I ordered my sink in 2019, though I would have been happy with the style and quality from either Havens Metal or Rachiele, both of which manufacture all of their stainless steel sinks in 316 grade, 16 gauge. All of these brands I've mentioned in this final paragraph feature offset drains locations, and the made-to-order brands will locate the drain on whichever side you specify. Copper sinks are another subject but may be worth investigating if you want a unique look and naturally antibacterial surface.
Q