There are about 4 types. You have the typical warehouse style forklifts, which are often propane, but increasingly electric; the stand up ones that range from 4k capacity, to almost an electric pallet jack with a platform to stand on; Lull/telehandler/shooting boom, from 4k to 12k capacity; and off road forklift, a reversed industrial tractor basically.
Nissian propane forklift are wildly available used, for cheap; but i would do some searching online for an out of service, auction, electric stand up, from Home Depot/Lowes, or similar sources. It doesn't sound like you need a lot of hours at a time.
It might be cheaper to do a raised loading dock/ramp, and a pallet jack?