We have white Corian countertops in our current house. We weren't sure of them when we bought the place, but they are REALLY easy to care for. Sometimes there are stains from cooking, but we use soft scrub and leave it on a minute or so and everything has come up without a problem. I don't know how that would work if you had a dark countertop. Same with scratches. If you look VERY carefully you might see a scratch on the white, but nothing noticable.

Well, my current kitchen has white solid surface counters from '96. I loathe them. They scratch, they stain, and if the stain gets into a scratch not even the scrubbies get them out. I would never, ever live with white solid surface again. If I couldn't do some type of real stone, then I would definitely go for a darker surface, preferably with some type of slight pattern - our children's hospital has dark blue with teensy white/silver flecks that is quite pretty. But never again a plain color, or a light one.

I have light beige granite-look Swanstone. Doesn't stain and scratches, if any, are unnoticeable. Been in since 2003, love love love them! Invisible seams and super easy to clean.

Was surprised and pleased to find they are great with pastry, too.

Oh, I do cook a lot, so have scrubbed off curry stains, chile stains, purple dye, etc. They can sit for days but everything comes out with a green scrubbie - I have a beige Swanstone sink as well, and that doesn't stain either. Worst is rust from cans, that takes a week or so to fade away. For some reason it won't Softscrub out, but just fades on its own, as a few days go by.

I had pink Corian from the 80s while I got around to a remodel. I abused the heck out of it because I didn't think I'd have it for long. Scratches didn't show due to the speckled pattern (and wouldn't show in a light colored Corian either). It didn't stain. The sink was an unspeckled pink and it did get grubby looking after having dishes sitting in it for a long weekend or cast iron pots being left to rust but it would always come clean with little effort. I didn't have the heart to put it to the burn test.

You can sand out/refinish these counters. Yourself.

The integrated sinks are really totally wonderful.

Don't get pink speckles though.

Corian scratches very easily. And cracks. I've had both dark and light in two different houses and either way you will see scratches.

Integrated sinks are all well and good - but you can't replace one without replacing the other. Just sayin'.

It's not especially easy to replace anything but a drop in sink.

Well, it may not be easy, but it can be done, usually. One can replace counters without replacing a sink, for instance. There are pros and cons to integrated sinks and the big thing is to be forewarned as to which trade-offs one is willing to accept.
We have integrated sinks with solid surface in the bathrooms from the PO, and solid surface counters in the kitchen, and I hate all of them. The kitchen's are white and are pretty beat up, the master bath has cracks in one sink (not leaky though) and a few indelible stains. The kids' bathroom has held up pretty well, but the 4" backsplash on either side of the counter was not even fitted to the counters before being glued on so they look awful.

So, definitely cons to consider at least for the OP.

I am okay with my corian but I would not buy it again. I was just not prepared for how easily it marks up. I stopped worrying about it about a year after we bought it and I just figured I will have it rebuffed before we sell.

I thought Caesarstone was quartz?

I've had no-label made-in-China white quartz for a few months. I've left tomato sauce, jello powder, red wine, blood, curry, oil, etc sitting on the counter and there's been no staining. My nephew drew on the counter with a marker and I didn't see it until the next day, and it wiped right off. The only thing that leaves marks is rust. It comes off eventually.

Heh. And since I guess "solid surface" is the plastic stuff, I'll add that I have Corian floors in a couple bathrooms, and it's been very easy to care for. No staining. Some scratching, but nothing you'd notice. We don't baby our floors.

I think there are several answers to your question and I will try to tell you in detail about each of them. First, I think you should think about the coverage, because this is probably the most important factor. It's important to prevent the problem before it even occurs, but I think you already know that.
I can't think of anything more so than stainless steel. And as I thought about this answer it occurred to me it must be the reason commercial prep kitchens use it so much.
Solid surface countertops are synthetic and don't offer the same quality and durability as a natural stone. However, these materials are non-porous and don't stain easily. Certain chemicals and acidic foods can stain these countertops if left on the surface for long periods of time.
The second is this immediate caveat:
-Stop using acidic cleaners or heavy alkaline cleaning material that can strike and destroy stones.
And the third is a solution to the problem. To be honest, I have never encountered such a problem, but after a little searching on the Internet I found an article that might be useful to you: how to remove stain from solid surface countertop
To be honest, I do not vouch for the correctness and effectiveness of the methods described there, but personally to me it seemed the most correct and logical solution to the problem, so I recommend that you read this article and draw your own conclusions. I hope my comment was helpful and you can clean the surface without any problems.

"Solid surface countertops are synthetic and don't offer the same quality and durability as a natural stone."

Nonsense. There are tradeoffs on every surface. Try thermoforming stone. Solid surface is inconspicuously repaired; stone may or may not be.

And no, solid surface, unlike natural stone, does not stain.