Verizon charges less for post paid than prepaid.
From a best guess standpoint, Verizon requires a credit score of about 550 to get a phone package.
People in the neighborhood of 550 are required to submit a deposit.
The catch 22 situation of getting a good deal so you have enough to pay for pre-paid minutes is tough. Getting a credit report before going to the store is a great idea.
Verizon friends and family invites the "joint account" pitfall. In a situation where everyone is responsible for keeping under the minute plan, no one is accountable for staying under the plan.
Look for a corporate Verizon store and befriend the store salesperson. Visit during an off peak retail hour (ie don't go during evenings and weekends). If you only qualify for a pre-paid plan, then make it a campaign to get to the level of minimum credit required. It'll save you money.