The part of me that is FiberGeek must address the question of High Thread Count.
First, I don't know why this is, but I hear fellas talk about high thread count more than I hear women talk about it. Usually I think it's in the context of "impressing the ladies" (or whoever) by providing classy sheets. At times, it's been a question: "Should I get satin sheets? Or should I go with some High Thread Count? What would impress a new girlfriend more?" First of all, NEVER go with the satin sheets. Why? Two reasons: (1) They're usually polyester, which means they won't breathe, and that means unpleasant sweating -- not the good kind. (2) Someone will slide right out of bed, and that's never good. Oh, a third reason: (3) Icky, and trying too hard to look suave. Never works. Or backfires altogether.
But here's the point of this post: High thread count is one marker of a soft sheet, but it's not the only one. HTC alone is not the be-all and end-all of sheetness. It's better than those burlap sheets you have now, of course. And if the HTC sheets are all-cotton (and not a cotton-poly blend, which defeats the idea anyway), then you're doing reasonably well.
But there is another essential factor to excellent sheets, and that is staple length. Whuzza?, you may well ask. You see, there are various species of cotton. Some have short fibers and others have long fibers ... that is, their staple length varies. As an example, take a cotton ball in one hand and pull just a few fibers partly away from the ball and twist them between your thumb and forefinger. As they twist together, pull slightly further away from the ball, trying to pick up some more fibers into the twist as you go. This is essentially how threads (and yarn) are made. A cotton ball is made (I assume) from waste fibers, so they're varying lengths and mostly they are very, very short.
Most fibers, animal and plant alike, have microscopic little barbs on them that catch onto other fibers, which is how the twist holds in threads and yarn. (This is why your pet hairs stick to your clothes, furniture, and carpets too.) Short staple cotton will hold together all right (when twisted with more oomph than your fingers can provide), but, as you can imagine, they might break more often when they are very, very thin threads. If you get HTC sheets with short staple cotton, you will find after a few washings that they start to pill or feel slightly rough to the touch. This is because the short staples are starting to break apart and pull away from each other. The sheets will still feel great compared to other sheets, generally, but they are likely to wear out and tear in a relatively short period of time (depending on how you treat them, of course).
So, what do you use instead? Long staple cotton, of course. Egyptian cotton is the standard bearer for long staple cotton, and sheets (or clothing, or towels) made from Egyptian cotton are likely to be very expensive. An American version of Egyptian cotton is pima cotton (be aware that fiber content can say "pima" but not be 100% pima -- look for "Supima," which is required to be 100% pima). However, durability is exceptional, and the hand of the fabric (the way it feels to your skin) is out of this world. Towels made from Egyptian or pima cotton are tremendously absorbent and luxurious feeling. Sheets and clothing drape well and last for ages.
Another option in the sheet department is linen -- long-stapled by nature, a HTC linen sheet will also be very expensive, should last a lifetime if treated properly, and feel amazing.
Personally, I can't afford to buy fancy sheets and stuff. However, if you can afford it and want to really impress your sweetheart, think about going for the long-stapled stuff.