If you don't have a personal bank account and a debit card and/or credit card, get one set up as soon as you can so you can start building some credit history and financial presence. Sometimes you can piggyback on a parent's account to get a credit card. Charge something every month that you'd be buying anyway, and pay the full amount off every month.

Get a driver's license if you don't have one already.

Get either the original of your birth certificate, or a certified copy. Get your original Social Security card.

Register to vote as soon as you are able. If you are a guy, register for the draft.

Keep good records of your employment history, especially of the names and phone numbers of people you'll be listing as references on you future applications.

Look into taking a community college class. Sometimes having student status and a student ID will get you discounts or the use of resources like campus libraries/technology/gyms.

Establish residency in your new state by getting a new driver license and registering to vote. This will be critical if you ever need to apply for help like rent assistance, health care, food stamps, etc.