You can do it with about 1" of plywood. Cut your base about 10" square and mount the press to it, using flush mounted bolts from the bottom. I picked some up at a surplus sale along the highway a few years back and they work great for this type of mounting. You just have to inlet the plywood enough to allow the head of the bolt to be flush with the surface of the wood. I use large "c" clamps to mount the press to my bench. All my shotgun loaders are mounted this way, along with some other tools that I don't use a lot. They store on the shelf until needed, but my other three loading presses are mounted permanently to my loading benches, as they are used daily.
If you can't locate 1" plywood, you can take several layers of thinner plywood and glue them together to make the thickness you desire. Just put lots of glue on them and then clamp them together until dry and you'll have the plywood thickness you need.
If you don't have flat head bolts, you can use either carraige bolts or hex head bolts and fender washers to provide a larger surface for the bolt to hold to. If you use the thicker head bolts, then just add another layer of plywood to ensure you have enough "meat" for the press to mount to. Just remember to mount the bolts from the bottom of the wood and the nuts go on top.
Hope this helps.
Fred