A couple of things: a reduced load your first year or so is warranted if you're engaged in a lot of new prep. If not, and if it's not, say, moving from a quarter system which causes whiplash, then you might forgo it. But use any acclimation time / easing you can.

Second, I was offered 3k to cover the opposite move (South to Pacific coast). I asked for 6k, but only stayed in that range by doing U-pack carriers. I had a 2br apt, 15 years ago. Get them to agree to a higher reimbursement cap max, and go full-service. My move sucked, and I was living out of boxes for six months. One time money is easier for most departments to find than recurring funds, which are tangled up with approvals at most schools.

Salary: ask frankly how much room they have if you're nursing loans or something, but naturally don't push unless you have a competing offer.

(Congratulations, in any case--way to go!)