Everybody is talking about luxury high-thread-count sheets - and I do admit, I like mine, I buy them on steep discount at Tuesday Morning. But overall, they are not the sturdiest sheets, especially the really soft fine ones. The sturdiest sheets are the cheap polyester blend ones I used to buy in my student days - those suckers lasted forever. You could probably find them at Target or Walmart or such. Polyester is pretty tough, I have polyester clothes that have lasted decades. You won't get that luxurious feel though.
If you DO want luxury sheets, I'd avoid sateen ( I've bought some very nice sets that pilled almost immediately) and stick with cotton, no bamboo or rayon or silk.