I would try first paying those collections - open collections can kill your score. I know it can take awhile to post once paid, but hopefully you'll get a better rate because of it. Plus, once they're paid, the more time that goes by, the less impact they have on your report.
I don't claim to know a whole lot - I've been studying the ins and outs of FICO since my epiphany about two years ago, and still learn something EVERY WEEK. However, I will say don't go out and get a bunch of new accounts simply because you can-it's a recipe for disaster should something happen. There are lots of creditors who love people like you (I was you years ago, and on bad advice opened any and every account willing to loan me anything, establishing history, or so I thought). Take a couple, show good history with them, and take things slowly. You don't need a ton of history, just a good history.
I regularly council folks I work with on the very basics of establishing history for the future (by and large, folks fresh out of HS), and I always tell them not to bite off more than they can chew in the beginning. Remember, a good balance is important too. I've seen people with one CC show a 700+ FICO, and tell them to keep up the great payments. I'd have loved to be there at 20 years old! All you can do from there is go up with good practices!
Take the time to pay the collections off, pay good on what you have for six months, and watch that score rise. I now own two vehicles, four decent CC's, and my own brand new house, all well within my means, and it's thanks to the best advice I've gotten when it comes to this stuff: patience and prudence! Good luck...