Higher thread count is not necessarily going to get you a better sheet. Long staple cotton percale at a 200TC is going to feel better longer than a lot of higher TC ones. Those high thread counts are often produced via skinny, multi-ply threads.
Lands End has an Italian percale that is to die for (ask to be buried in your sheets). If you want to go really old-school, there's Red Land Cotton, but those are a little above what you want to spend:
https://www.redlandcotton.com/products/back-to-basics-sheet-sets