For your first concern, you could always post a listing first. When potential buyers contact you, let them know what your situation is and that you'll complete the transaction as soon as you move your number to your new phone.
As for transferring numbers, I'm not on Verizon but ircc my friend who does this every so often says that it's pretty much that, to disable your old phone and to activate the new phone by calling up Verizon and giving them the serial numbers (IMSI numbers I believe). This shouldn't affect your contract either.