Yeah, I agree with another poster- start off with a blush or rose wine- chill it. NOT TOO COLD, but chill it a bit. With spring here and summer coming, a chilled blush/rose wine tastes refreshing and light and it's really fruity.
Reds give me a headache too! I love whites, blush/rose, sparkling wines.
When I got into wine a few years ago, a friend of mine suggested finding a winery or two around my area to do my own tastings and see what type of wine tastes I prefered. It was the best advise I got and the best I can give, because EVERYONE has a different taste in wines. A wine that I LOVE may be hated by someone else...We have about 5 wineries with in 2 hours of us. We show up, do a tasting or a 'wine flight' and as we do them, I write down what I like and dislike about each wine. There have been some surprizes for me, because there are some wines I thought I'd never like and they end up being a favorite!
NOW, if you're talking about wines that you serve with food- well...your flavor demands will change. You'd never want a light,fruity wine with a heavy flavor meal- you'd want something that 'compliments' your meal, not something that will fight with the flavors.
The rule of thumb (which doesn't have to be followed)...a person who knows a little about wine will tell you that a heavy, red meat should be served with a red wine. Now, I've found a few whites that match the flavor, but that's my flavor and taste buds choice. Also, they'll say to choose a white wine with things like light meals- chicken, fish...but I've done the opposite of that on occasion as well.
Here's a site I've used occasionally...
http://www.foodandwinepairing.org/
Hope you find one that you enjoy! Wine is a lot of fun.