Check on switching your utilities earlier than you'd think you'd need to. It no longer takes 3 days to get electricity or DirecTv turned on somewhere.
Anything you've got left to purge, don't take anywhere- Box or bag it up and call one of those charities that will come pick it up from your porch and leave you a tax-deductible form. There are plenty of those- the Leukemia Society, veterans' groups, etc.
If you've got smaller animals (cats, Chihuahas, etc.), make sure you put them in carriers when you actually move them to the new place. Yes, it's not far, and yes, it feels like a big pain, but it'll keep them calmer during the ride and you don't risk one of them bolting for the hills when you open the car door. PetSmart and Petco have cardboard carriers very cheaply if you don't want to invest in a bunch of "permanent" carriers that you'll just have to store while you're in the apartment.