Just .50 worth of advise (adjusted due to inflation. )
Disclaimer: I will not comment of Lee Products other than the APP press and the old round tray Autoprimes. As thats all I have.
Progressive Presses whether Blue, Green, Red, Black, Pink, Rust colored, all need tweaks somewhere, all have their Pros / Cons, and of course their "Followers" all produce a completed round if "you do everything right and setup properly " with that said......
Single stage presses .. would be where I would start. While the amount you state is high it still would be a place to start one process per handle pull, less can actually go wrong vs. Progressive.
I've done "batch mode" as mentioned, case prep, hand prime, etc. with single stage, everything has it's place, prime only what you plan in a sitting to completely finish, so from that point prime, charge, seat, and or crimp
At one point in time I had several Rock Chuckers for my version of progressive as they were out of my reach cost wise. One size, one seat, one crimp. " we" would get together and have a "reloading session", bring your brass, primers, powder, bullets.
Single stage for you, start / load development, etc. Progressives it may take a little time to figure out what went wrong. Things can go wrong with just about any press / operator
Progressives... increased production and saves what everyone is so stuck on "time"
You can get into "added costs" most with Dillons have xtra tool heads to save time and make the "swap" easier, where as Hornady uses a "bushing" system, twist and turn to insert dies and remove them. So tool heads vs. Bushing system.
The above is basically up to the reloaders wants / needs.. determine that for the present and the future down the road.
Dies. Depends... use RCBS dies mainly, then Mighty Armory, and Redding.
Could go on about other things..but just some thoughts.
Presses, Texans, Hollywood's, Stars, CH, Dillon 550 / 650, Hornady Pro 7 / Projectors / LNL-AP', RCBS, Redding, Forester, and the ole Ideal-Lyman "nut cracker" out of all the presses it would be my Stars first. Just a well built piece of machinery.
Bottom line its what works for you and what your comfortable with, personally I dont care who makes it, its what works for me for almost 60 years.
To add:
Find somebody who will let you "pull" the handle on different presses and go from there.
Get several reloading manuals that would be a great help. As they may not agree. If your loading Hornady bullets use the Hornady manual, if your loading Sierra bullets use their manual, The Lyman reloading manual covers a lot different bullet brands, lead bullets, etc. I won't go into the details..but just because the bullet weights are the same and the description is the same, but are different manufacturers, re-think your loads
-Snoopz