When you apply for service, they will ask for your contact info, SSN, and a few other things. They will then check your credit, and based on payment history, you will have one of the following:
1) For good credit, no deposit, and no spending limit.
2) For not-so-good credit or no credit history, a deposit of up to $250 will be required, and a spending limit of between $125 and $250. After a minimum of 12 months' on-time payment, your deposit will be credited back to your account, and you can have them review your account, to see if they will remove the spending limit.
Whatever the outcome, it can't be negotiated. It is what it is.
As for your bill's due date, it all depends on the billing cycle that you fall into. There's no way of knowing that until the account is open. If your billing cycle is within a few days of activation, you'll be charged for the number of days in that current cycle, plus the next full month in advance, plus activation fees and tax. The more days between activation and end of the billing month, the higher your first bill will be, but also the later your first due date will be. Whenever it comes, you'll have about 14 days to pay the bill. And yes, because of the prorated month and the activation fee, expect your first bill to be much larger than the rest.
Be very careful if you have a spending limit! The limit is based on all charges on the account. So if you have a $125 limit for example, and your first bill has a $36 activation fee, a $69 plan, taxes and fees, you're going to be close to your spending limit right away. Be prepared to make a payment on your account (at least the activation fee) when you buy your phone, so you have a little more room under your limit. Once you reach your limit, your service may be suspended until a payment is made.
I know it's a lot to take in if you're new to a phone service with a contract, but I hope this helps.