In your case, unless you could find a moving company offering some type of short term storage special, the cost will kill you. I've seen companies advertise 1 week free storage with a full service move. You might look into it.
My sister used a door-to-door service when she moved a few months back. She said it was great. They dropped the container off, she packed it, they picked it up and trucked it to the new pad.
I noticed the PODS website does not offer much information.
See
They have a warehouse right next to my office, I'll see if I can grab a pricing schedule.
I would worry about the record collection no matter how it was moved, unless I did it myself. If you don't have a lot of other stuff to move, this may be the best route.