You can't use wines effectively as a cook unless and until you develop at least a rudimentary taste for them. Well you can, but it's unnecessarily difficult unnecessary unless you have an allergy, addiction or something similar. "I don't like wine" is all the more reason to learn. A civilized palate is part of becoming a decent cook.
The rule of not cooking with something that isn't drinkable has some flexibility. Like most cooks I cook with inexpensive but drinkable wines. However, the wines I drink are at least a step or two up from those I use for cooking. $5 a bottle is pretty close to max for cooking. $2/bottle Charles Schaw ("Two Buck Chuck") from Trader Joes' is the usual.
The red varietals I most often use are Shiraz (aka Syrah); Merlot; Pinot Noir; and Cabernet Sauvignon. Also, generic Burgundies; Beaujolais; Chianti; and "reds," such as "Big House Red," which is currently vastly underpriced. The defaults are Shiraz or Zinfandel when I want something fruity, and Merlot when I want something laid back.
For whites: Chardonnay (but not oaky, as vjbme said; Chablis, Riesling, Pinot Grigio; Frascati (hard to find, very crisp); Chenin Blanc; and occasionally dry, white vermouth which is not, properly speaking a wine at all -- it's "fortified wine." I most often use Chablish or Chenin Blanc as varietal whites; Traminers or Rieslings for something flowery and and spicy; and vermouth for dishes dishes big enough to handle its winey herbaciousness.
Hope this helps,