That makes it far more clear. I hope you're ready to bum out the cat when the litter box is moved....
One thing for sure. The press is best mounted to something that is fixed firmly in place. There's two ways to do that. One is to screw it to the wall and floor. The other is use gravity by making it heavy or by storing lots of heavy items in it.
So I'm thinking to get the upper storage that you want to put together a "hutch" style setup either with the lower area holding everything or with a separate upper support and cabinet that attaches to the lower unit.
You can either shop around for a cheap armoire that can be converted to a working area of this sort with the addition of a well secured work top or you can build something up. Either way the "ballast" you add in terms of storing the goodies and anything heavy you have kicking around should be stored well towards the rear of the unit to aid in counterbalancing the lever pressure. An armoire would need to be equipped with lots of good lighting because of the full sides shading the inside. But it's a way of getting setup for cheap. None of them are very wide though so it might be kind of tight.
Do you have a place or a buddy with a shop where you can cut and assemble some 2x4 lumber and cut some plywood? If so you might be able to make a break down bench that works quite well. I've got an idea in mind for a setup that uses two end frames and bolts stretchers between these to support your work top and a pair of cheap kitchen upper cabinets. It would all break down for moving with the heaviest piece being the laminated work top which would be around 40 lbs. But you need a shop to build this. Or at least a place where you can set up and cut some wood with a circular saw out in a big open area and make a lot of dust and chips. Plus you'd need the tools.
If you don't have any of this another option is that Home Depot shows a couple of options for 48 x 24 inch work benches. The one that has a peg board upper could likely be converted to mount two cabinets up high and move the light to just under the cabinet. HD has lengths of that angle steel with the holes in it for building such things which you could use to modify that bench of theirs.
https://www.homedepot.ca/en/home/search.products.html#!q=work bench
Kferguson makes a great point about the scale idea. Those beam balances actually work decently enough but it's so much better if you have them at eye level to avoid parallax errors. If you build up a bench with cabinet uppers I'd set it up so that one of the shelves is sitting right at eye height when you're seated on a stool or while standing. Accurate rifle ammo calls for weighing each charge individually so you want to make it so this is a comfortable setup to use.
Lots of ideas here but nothing hard and specific because you need to consider your options and tailor your final solution to what you can build, buy or who you know that will let you do this stuff.
