You will have more water on the countertops with a top mount sink not less. Corian tops with integrated sinks are awesome but no one in my market makes them either.

I think water on the counters is solved by like you suggest the single handle faucets and how you pick up your soap, dishrags etc.

The gunk around the seal can be prevented by install using a slight positive reveal (search the forum by posts for Joseph Corlett)

So I think top mount or undermount is your choice, but it's not closely related to your issues with past sinks.

I did top mounts in our reno although they are unpopular these days, I like them.

I have under mounts in bath and kitchen and have never had a problem with water collecting nor with gunk in the seam. Perhaps the undermounts you had were not installed well? Maybe the height or placement of faucet was incorrect?

I've been temporarily staying in a home for a few months with a drop in kitchen sink and I loathe it. Nothing beats and undermount where you can swipe counter crumbs directly into the sink!

" I also get tired of the guck that builds up where the granite meets the sink. it's not always easy to clean, especially if the sink is square."

If you have gunk at an undermount sink, that sink is leaking. Strap your undermount sinks and fabricate with a slight positive reveal and it's impossible to get gunk.

Here's an undermount kitchen sink in our last personal build.

Never a problem!

You've got me wondering why I have a drop-in sink ready for the kitchen on the current build. Six of the baths are set for integral stone sinks. Now maybe all of them!

Thanks for the push.

Water from a faucet shouldn't happen. Choose the neck dimension of the faucet correctly and you can avoid that.

I'm in the same boat, looking for drop ins due to mold in undermount sinks. Currently we have a positive reveal in our kitchen with granite and an undermount sink, we have mold in the visible silicone. Everyone I've talked to with undermount sinks regardless of the reveal has gunk and or mold.

I don't have gunk or mold in my undermount kitchen sink. And as for the "water everywhere" it's just a matter of wiping the sink area after every use - which is a very basic part of housekeeping.

Not sure if you’re still in planning mode, but I’ll add what eliminated 90% of eater on counter (by the handle and where the faucet inserts into counter. ) we purchased a single handle faucet and instead of positioning the handle to the side , we aligned it straight on with the faucet. Incredible improvement! When washing dishes or hands , it’s natural for me to turn off the water before drying my hands, but my wet clean hands would drop all over counter in the past. With this adjustment problem solved.

Here’s a photo