As far as renting, not sure where you'd be going (if it's expensive for housing or not) but you might be able to work with realtors on renting a house, explaining your situation or showing your bank account balance/paying a few months rent ahead of time or rent through an apartment complex that way. It can be tricky to rent with no current proof of income. There are long stay hotels that are studio like, with a kitchen and those can run about $50 a night. That can add up, but maybe OK depending on your situation. Some can be sketchy, some are OK depending on area. Some Airbnb's will let you rent for an extended time - but again, pricey. Last resort, probably renting a room from someone. Once you get an address/lease, something to show you live there you can update your bank info, get a state ID/drivers license/Voter Registration and so maybe you can get a PO Box (USPS wants to see you actually live somewhere), Cell phone so you can be reached for possibly job offers.
Once you get a job and start having income, like Lorenausuk says, you can probably start applying for secure credit cards, you may also be able to try for store cards as well. Car loan maybe rough with the high rates with no credit. Depending on your savings you might be able to transfer to a credit union, I hear they can sometimes do lower interest rates. Depending on your area that you move to and your money situation you may need to take public transportation for awhile or hoof it. All depends on your situation though.
There is some great advice about building credit on the
https://www.reddit.com/r/personalfinance/ forums, what and what not to do and people's experiences on how long it's taken them to bump up their credit.