UPS definately.
THey garuantee a delivery date- even for ground shipments as long as they are going to commercial addresses, which i would assume a hotel to be (and frankly I can count on one hand the number of times they havent hit their expected delivery date- check their website they have a transit time calculator to figure it out). and you can track the package without paying extra. For really small packages usps might be cheaper, but for bigger I think ups is best (could be wrong though so double check the prices if it matters to you). Also UPS is automatically insured to $100 for free- USPS you pay for any insurance- even the first $100.
Whenever we go, I plan to have the package arrive the day before we arrive, and bell services has always kept them for us, no problems (sometimes it takes them an hour or so to dig it out but you just tell them theres a package for you when you arrrive and they get it).
Also if you want overnight or 2 day shipping home you can get slips from ups and charge it to a ups account or to a crediet card. Than you just give it to the bellhop when you leave and they get it to the UPS driver for you.
Your beat for the air mattress- you'll need to pay for that somehow. But for shipping souveniers back- disney will take care of that for you. You pay shipping but no sales tax so if you bunch up your shopping to make each purchase a decent size dollar wise it works out to be almost free shipping home (UPS ground I believe).