Glass

Glass meets your criteria. Having said that, I had a glass dining table once and would never have one again. Glass is very uncomfortable to rest your arms on, the edge and corners are painful to bump into, and I feel it lacks warmth and solidity. But your taste may differ.

Thanks for your insights, Isaac. I totally agree. Glass would be cleanable, but not very comfy. What do most people do?!?

Life is full of compromises. No one material will fill all your requirements. Pick the ones most important to you. Personally I had several glass tops, rounded corners, flat, high polished edges. I loved them because the kids could paint and glue projects, but I could wash the surface with dish soap and water.

I will certainly consider the glass option. What do most people have? Laminate tops? Certain types of wood that don't mind getting damp? A special durable finish? Or do most wooden tabletops endure daily meals?

Hardwood with a good finish on it will be ok as long as you don't cut on it or let water sit, in my experience. Worst case, solid wood can always be refinished.

So I guess my next challenge is finding "hardwood with a good finish" in my budget. The rustic ones I like look too full of pits to keep clean, and the smooth ones look so vulnerable to damage.

You may be overthinking this. No material will be perfect. Check Craigslist - decent wood tables pop up there with some frequency.

Or get a tabletop fabricated by a local woodworker and stick premade (IKEA, hairpin, etc.) legs on it. Hickory is very hard and rustic looking.

I found the perfect table at Crate and Barrel. I got the popular Basque table in the Honey finish. The scale is just right for my space. I wipe it several times a day with a damp microfiber cloth. We've had it for several months, and it still looks as good as new! Recommend!