Hey friends!
As previously mentioned, I just moved across the country. I've started my oncology internship (which, btdubs, could not possibly be more different from my last internship), and today seems like an excellent day for a collection of moving tips for you:
1) Find a place to live.
It's actually much harder to rent an apartment long-distance than it is when you're moving from one local-ish place to another. Unless you have many dollars, it's probably cost-prohibitive to fly back and forth to look at potential places/meet potential landlords and/or roommates.
Landlords are more reluctant to rent to you (see: what if you see the place and instantly hate it when you get here?), and potential roomies are somewhat hesitant about signing you on (see: she seems okay on Skype, but what if she's actually horrible in person?). It's just easier for everyone to rent to local folks.
So! Jump on that. Search early and often. I'm a fan of craigslist, but others prefer sites with a broader net (such as Padmapper). Decide on your nonnegotiables (no basement apartments? rent < a certain $$? close to school or work), and call/email listings that look promising right away.
2) Get rid of your shit.
No, seriously. You probably have a lot of shit. If you are legitimately moving across the country (or a similar distance), it's gonna be more expensive if you still have a lot of shit come moving day. Make a "thrift store" box, a "sell" box, a "throw away" box, and get sorting.
3) Decide how you're going to get there.
Are you driving? Renting a moving van? Flying? Flying and selling your car? Flying and shipping your car? Taking the train? Decide which mode of getting yourself to your new city works best for your lifestyle, traveling companion(s), and budget.
4) Decide how your belongings are going to get there.
I'm going to tell you something (as this person has already mentioned) - Amtrak is a secretly excellent way to ship your non-electronic, non-furniture items. I shipped 38 boxes across the continental US, and it cost just under $500. At the time of this writing, the cost was $72 for the first 100 pounds, with each additional pound costing 73 cents.
In theory, you cannot ship more than 500 pounds per shipment - however, at the Amtrak station I used, the gentleman did not enforce this. You also are not supposed to ship furniture or electronics (anything with a cord). The maximum size of a box is 36"x36" - bike boxes are exempt from this, but they count as their own shipment (I'm not 100% clear on the bike rules, as I did not send my Surly on the train). The boxes arrived when they were supposed to, and only one box had some minimal damage. Winning!
5) If at all possible, set aside some funds for the move.
There will be a fair few planned expenses (travel, shipping, +/- hotel, takeout after you pack your kitchen, etc) as well as some surprises. Any cash you're able to save for moving and associated costs will help reduce your panic and make the process a bit easier.