Two years ago I moved from Virginia to Arizona with nothing but a plane ticket and what could fit in a suitcase. It is very hard to move to a new state without knowing someone there. I say that not to dissuade you, but to prepare you. ~~~~
Job: It's a bit tricky looking for a job and a place to live at the same time, since you need an address to apply for a job and you need proof of income to apply for an apartment. I stayed in a hostel for a couple nights then got a room in a shared house until I got my job and my apartment (roommates can be a lot more relaxed than landlords).
Rent and utilities: It depends on where you go, but deposits and start service fees add up quickly. So not only will be be paying first and last month's rent, but also a deposit, plus maybe an application fee, plus a possibly deposit for any utilities you pay separately (electric, gas), plus a start up fee for those utilities and for internet.
Car: You'll have to switch your car registration and your drivers license over to the new state. There will be fees for both, you might also have to pay taxes with the registration. Amount differ by state. You'll have to notify your car insurance of the change in address and it might make your premium change. Also, different states have different minimum required coverages so check on that.
Furniture and stuff: Either you have to move your stuff, which means you'll have to rent a truck and then probably find a place to store it until you have somewhere to put it, or you'll have to get new stuff. Either way is going to be expensive, and even if you do bring your stuff, you'll inevitably end up needing to replace some of it or add to it. Different home, different layout, whatever.
Lost income: The lost income from not working during the move will likely be the single greatest expense and, unless you have a job set up when you get there, you can't predict how much it will be. Two weeks? Two months?
Actual moving expenses: Gas, motels, eating out instead of cooking at home, having to restock your kitchen in the new place.
Bottom line: It will take a lot of effort, and it will be financially and emotionally draining. I do not recommend moving to a place you've never been unless you are willing to move again (along will all the effort and money that requires) if things don't work out. All of that said, I think it's a great idea and I think it'll be an adventure and immensely rewarding. Good luck!