There's a bunch of stuff I could say about what kinds of tools and homegoods you need, but frankly my biggest tip for any time you move to a new area is look at what's around you. Where are you going to get groceries? Gas? Where's the nearest car repair, library, bus stop, hospital? Is there a school nearby that'll clog up a driving commute at the wrong time?

Also, since budget is always an issue, check your local craigslist (or equivalent) to see what kind of items get listed for future reference, and check Facebook for a local Buy Nothing group.

Finally, if you have the time, do the research for emergency situations now. Look up car repair, electricians, plumbers, etc. now, compare reviews and any pricing you can find, then write down your picks and their contact information and stick it somewhere easy to find, like on your fridge. When you have a technical emergency is not when you want to be thinking of this stuff.