For my money, the best sheets for both softness and for not wrinkling is 100% Egyptian combed-cotton percale with a high thread count—over 600 if you can afford it, but under no circumstances under 250. Your sheets will get softer with every washing.
What thread count is the smoothest?
Thread Count Matters
Good sheets can be found at the 200 to 250 thread count range, but the ones that look and feel the smoothest occur in the 350 to 500 thread count range.
Is 400TC better than 200TC?
The rule of thumb is that anything above 200TC is very good quality, and anything above 400TC is not necessary and just brings a bigger price tag with a compromised experience. The same rule applies to organic cotton bedding too - 300 TC is considered in the luxurious, premium range.