I reload for pretty much everything I shoot... .45, .44Mag, .44SPL, .357, .223, 7mmx57, .243, 8mmx57, 7.7 Arisaka, 7.62x54R, 7.62x39, .30-30, .30-06, .308, 7mm-08, 7.5x55, .444 Marlin, 12ga, 7mm Rem Mag, .357 Moleman, 300BLK, 6x45, probably a few others that don't come to mind right away.
You won't go wrong learning on a single stage. I've got - and use, and like - LEE, but it's tough to beat an RCBS single-stage. Get the Rockchucker kit, some LEE dies, and a few extra reloading manuals. Speer, LEE, Hornady will cover you to start. What I like about the LEE manual is that it doesn't try to sell you Alliant powders or Hornady projectiles, etc., it's just a good all-around reference. But it's important to have and refer to multiple manuals when developing a load.
Once you have your technique down on a single-stage you can start messing with progressives. The Dillon owners love them but I don't do enough volume to justify the expense and setup time.
As you can probably guess from my list, my main interest in reloading is to feed antiques and milsurps, and oddball wildcats with no factory ammo available.
If you want to make the plinking and practice ammo for cheaper than you can buy it, you absolutely can. That's one direction to go. The other direction is accuracy, or velocity. On rare occasion you'll be able to make a highly-accurate load that's cheaper than factory but generally the continuum is: "cheap ammo - factory ammo - accurate ammo". My focus is generally on mild-recoiling plinking ammo and reliable hunting ammo; I generally don't take the time to chase the last few .01" of accuracy but have mad respect for those that do. Once you start down this path you'll sort out your own priorities and motivations and load accordingly.