Homebrew isn't where I would start, unless you already knw somebody who brews. If you want to expand your beer horizons, go and see if you can run down some commercially produced craft beer.
Understand, there is a LOT of variance within beer - check out this
beer style guide. Most US beer is "American Light Lager", but there are MANY more types. I'm personally partial to English and Belgian ales.
Our local Publix grocery stores have a great thing going - you can build your own six pack of beer for a flat rate of $9.99, and put almost anything that they stock in it. This gives a superb chance to try different styles. Some higher end package stores will do the same type of thing. That way, you don't get stuck with a lot of beer that may not appeal to you.
Also, note that when drinking beer, don't just pop the top and drink from the bottle. Take a glass (beer glasses are best, but any glass will do), make sure it is REALLY rinsed out (detergent residue kills the bubbles in beer), and pour the beer into it.
Beer in a glass allows you to get the aroma from the beer (you will smell grain and yeast, then depending on the hops used, you might smell grass, fruit, or a host of other scents). The smell helps increase the taste (if you don't believe me, hold your nose while eating sometime).
Also note that most beer is a little better when served a bit warmer than typical fridge temperatures - ice cold is for beer that lacks flavor.