I understand many people are intimidated by the thought of buying art. Intimidated to go into a gallery to even look at art. Art shouldn't be intimidating. There is so much art out there to look at. Prices are great too. Most people think that to get an original piece of art will cost a fortune. Not so. Sure there are well established artists and their work sells for thousands but there are so many artists just beginning their careers and their work is very reasonable. How reasonable? About the same cost for a hi-end poster or art reproduction. Maybe less.
There is a lot of art on the web. Check out flickr and type in the type of art you are looking for in the search pane. Tons of artists on Myspace as well and countless other on-line galleries. Most galleries are on-line as well.
If you find an artist you like, shoot them an email to see if they have anything for sale(if they don't already list their work on their own site).
Go to local galleries, go to galleries when you are on vacation, go to art fairs, whatever.
As to what type of art to buy, well that's up to you and your tastes. Forget about art as investment and just buy what you like. Maybe you start a collection of art of one type of animal that you like. Or, art that is all the same color. Or, same general style. Or, landscapes. Whatever floats your boat.
My personal collection (still budding) is quite eclectic. I just get what I like at the time. I'm an artist but I don't necessarily want to look at my own work all the time. I want to be inspired by the work of others.
So, go forth, look at all the art you can and buy what you like.