Typically the only thing that really decides whether or not you're a customer is your credit rating so when your credit is run they will of course know about the past collections however if your credit is in good standing you should have no problem becoming a customer again however your credit limit might be lower at the beginning.
As mentioned, it will depend on your credit. Prepaid could be an option though, depending on whether or not you want the perks of a postpaid account or plan. If your credit isn't stable enough for postpaid, you could see if someone else would add your line of service to their account.
I see you got so great advice from some of our members. Did you have any other questions about setting up an account?