Armourall - there was an "off" style of smaller dies sold by Ideal (?) - which was mostly taken over by Lyman - I think there are adapters to buy to go from 7/8" normal thread to that unusual Ideal size. But other than that, can run into the really fat dies - like for 50 BMG or perhaps 12 gauge - the RockChucker here has an adapter threaded in to use 7/8" dies in that press, although the press is threaded for the really fat dies. As mentioned above - I have RCBS, Lee, Lyman, Hornady and even elderly Bonanza (!) dies that all screw in and fit to that adapter without issue.
As you work through various presses, you will find there are "single stage" - so only one operation per die set-up on the press (versus turret styles that will let you set up multiple dies at the same time), or "single leverage" that have a simpler mechanical system - versus "compound leverage" that will generate much more force within the press for same effort on the press handle. I have never used a "progressive" press, but I think they are like a turret press, that advances the "turret" with each swing of the handle. I do not know what leverage system is used on various "progressive" presses.