Well depending on your budget, and how new you are, I think most folks would agree with me that you might want to shop used. You'll get two to three times further with your money that way, and if you decide bass isn't for you (IDK HOW new you are to it) you won't get slammed with the huge loss you take selling something you paid for new and barely played.
That said, if heavy or big isn't a problem, you can pick up used peavey combo amps really inexpensively. Lately the Ampeg and GK combos get lots of love, too. The Guitar Center brand Acoustic has some decent offerings in the inexpensive range, as well as Kustom. The 1x15 combos will have the oomph to get you through playing with other musicians. The smaller ones like the microbass and minx (peavey), the ba1x10 and 1x12 (Acoustic and ampeg) and backline 1x10 and 1x12 (gk) might do you well, but hit limits with some drummers. Like B said, I would shy away from less than 40 watts and smaller than a 10" speaker. If you KNOW it's only for you, at home, and not going to be used for playing with anyone else, almost anything in an amp will do, but look for headphone output and cd/mp3 input.
It seems a bit intimidating at first, but you'll figure it out. Play stuff. Don't be tempted to crank the low end on the eq, and don't be scared of turning up the midrange. Most of all, practice, practice, practice, and HAVE FUN!