I'll try to be short here, but you really don't want a small, walk-behind model. You'll need six trips to get from point A to B and each trip will take anywhere from two to four times as long as it would with a full sized skid steer of some sort.
If you need a machine to lift 3,000 pallets, then you really should consider getting that big of a machine. Unless you have experience breaking down the pallets and knowing how to split one pallet into two pallets (so you can carry the objects) without their falling through the fork openings, you probably want a 3000 ROC machine.
But... if you really want a 1500 ROC machine, there are a few that stand out in my opinion. I don't recommend going with a radial lift machine as they can be quite tipsy (especially if you are off-loading off of a flatbed). If you go with a radial lift machine, I suggest going with a 1750 pound-class machine, such as the Cat 236B. If you are used to hand controls, try the Case 40 or 60 XT (probably the 60XT). Bobcat doesn't have an offering in this category, but the S160 is the closest thing they have. If you choose to go with Deere, their 317 will do everything you need... potentially even lift the full pallet without tipping. (That's a maybe, not a definite.)
As for vertical lift machines: the only vertical lift model that is 1500-ish ROC that I can think of it NH, and I really don't have a very good image of their smaller machines. The larger Ls180 and Ls190 aren't back, but the 150 and 160 may be too small and slow for your needs. Their design seems to be shorthanded.
Let us know if you have other questions.