My company moved me from Portland, OR to Washington, DC. They basically gave me a set budget and I had to fit everything in under the budget (or pay for it myself).
The budget allowed my girlfriend and I to hire movers (although we packed ourselves), ship one car cross-country, pay for food, gas, and lodging as we drove our other car across, and stay in an extended-stay hotel and pay for a storage unit for a month while we looked for an apartment. The budget was a good amount considering my position in the company at the time and the fact that I was not married.
The whole experience wasn't too bad. In my case, I needed to have cash on hand because I was reimbursed for everything except the movers, who billed my company directly. The movers (United Van Lines) did lose one box and break the glass in my entertainment center.
One thing that surprised me was that in Virginia, there is sales tax, and Oregon doesn't have it. So when I went to register my car in Virginia, they told me I had to pay $500 sales tax because I had owned the car for less than a year (8 months) and I hadn't paid sales tax on it. This kind of pissed me off, but luckily my boss agreed to pay for it because it was an unexpected cost of moving here.
Also, be sure take a look at some cost-of-living indexes and be sure your salary will cover your lifestyle in the new city. Housing costs, especially, can vary wildly from city to city for a similar place.
Overall, I think living in a new city has been a good experience. However, I still love Oregon and I'll be moving back someday unless my career here really takes off. My friends and family are all there. Still, I'm definitely enjoying my time out here. Good luck with your decision!