The general rule about cooking with alcohol is to use an alcohol you'd drink. That doesn't mean going all-out on a fancy bottle to braise with; all it means is that you should use something both drinkable and intended for drinking.
If you don't drink wine, buy half-bottles; they'll keep in the fridge for up to a week, which gives you time to choose another wine-using recipe.
There's a saying that "what grows together, goes together" -- choose wine from the region your recipe comes from for a guaranteed flavor pairing.
When you reduce wine, you amplify all the flavors. That means that if you want a sweeter sauce, choose a sweet wine; if you want a jammier-tasting sauce, choose a fuller-bodied wine.
Cook wine for at least a minute or two after adding it to a dish -- without that, the wine can overpower the other flavors in your food.