Oh, right, tannin's drying sensation! Well, tannin comes from the seeds and skins, and is most present in red wines. Red wines are 'in' right now, especially Bordeaux, but whites are good too! Don't ignore them.

In fact, Suauterns, a white bordeaux is a sweet desert wine with a distinct taste produced by a certain kind of rot. (!) It can be some of the best, most exalted, and most expensive wine in the world because of how hard it is to get juice from these raisinated grapes, and how hard it is to harvest them. Tokaji and beerenauslese are similar in that they are sweet, rich and use botritis affected grapes as well. The taste is distinct and a bit musty.

Ice wine or late harvest wine are cheaper, and don't have the challenging taste of noble rot. Cheaper is relative here, because you will NOT find value in desert wines. They are pretty much all hard to make and expensive.

The best icewines come from Germany and Canada, and they are so expensive because the grapes are literally frozen when they are harvested, and only a little bit of juice comes out. The best of wines can age for years and develop distinctive character.

The closest that you can get to value in the sweet wines category (without going to sweetened wines, coolers etc) is late harvest wine. Some vinyards that do icewine make a late harvest wine as well that will have some of the same character, but are less sweet and rich, made from non-frozen grapes.

Anyway, have fun!