Just went through it myself. It's worth the expense for a professional firm that comes in, pacts it up, trucks it and then delivers it to the room you designate. Clean house ahead of time and get your shit organized because they will put only one name on the box and if you have Christmas decorations mixed in with that special pocket knife you have you won't find it until next Christmas.
As far as the safe goes unless you can pour concrete over steel reinforcing and then add the door, go with a good safe. Get it before you get the estimate from the movers.
And by the way, Move all your firearms in the back of your car. They won't pack ammo either (although I had so many lose rounds and shit they couldn't identify (a case of primers) they packed some any how).
Where'd you move to BTW?
Email me.