You have very limited options, - one actually - renting - this is possible with the right landlord.
Run in the opposite direction from any idea of "rent to own" - I won't take up space now telling you about all the dangers lurking for you (or anyone) in that arrangement .
You will not be approved for a loan, so buying is out of the question for the time being.
Truthfully, until you get your finances straightened out, you shouldn't even think of taking on more debt at this time(even if a seller were willing to offer you financing)
You need to concentrate on finding a landlord (not a management company, but it can't hurt to try) who will be sympathetic to your plight and happy to hear your jobs/incomes are stable.
If you work with an agent, they can help you find that landlord, and perhaps suggest ways you can offer him or her piece of mind in renting to you under the current circumstances. Maybe some upfront additional rent if it's allowed in your state (NJ doesn't allow that above 1.5 months rent). A letter explaining your situation might also prove useful. Personal references may come in handy, too.
May we assume you have money for the security deposit and any additional required deposits/upfront rent? If you don't, then you really need to sit down with an agent and try to figure it out.