It depends on your aesthetics. You could choose framed prints of your favorite works of art. You could buy prints or originals from artist friends. This time of year there are usually events where artists sell their work - art fairs, fundraisers, shows, open studios, etc. You could also go to an antiques shop and find an old painting if that fits your taste.
There are several websites where you can find original art and prints by contemporary artists. Buying art doesn't have to be expensive.
One bigger piece you really love is worth a few you feel so-so about, but don't feel pressured to go big, either. Small work can be more intimate.
If you have no idea what kind of work you like try browsing art museum and gallery websites, or even Pinterest "art" and "fine art" boards. Something will speak to you.
If you have no idea how to hang it, again, peruse blogs, Tumblr, Pinterest, etc for interior design.