Well, I'm gonna throw in my 2 cents. Based on the cartridges you have listed, IMO, you need a turret press. I say this because I don't shoot competition matches but have loaded handgun and rifle. I have thinned down over the years to only .45ACP and .223 for high volume plinking rounds, but a turret easily does 250 rds an hour. I only get out once a month or so, so that allows me to blow off 5-600 rds if I need to and not have to spend forever making them shoot again. But, a turret can also be used as a single stage to produce hunting or precision rounds for rifle.
Don't let anyone fool you, Lee makes good gear. They sell just as much as anyone else, most times for less. Many compare their presses against the "Lee junk" that costs a quarter of what the big guys are selling their stuff for and will load good ammo. Want to have better quality and STILL spend less than the bigger guys? Buy Lee Classic Cast instead of the value presses/kits. Those presses are just as bulletproof as their far more expensive counterparts. You can load .50BMG on a Lee Classic Cast single stage press. Not so with a RockChucker.
I started with NO budget. Second hand equipment (Lee) and loads of time. Using friends' gear at their place (gun club had a room set up over a member's shop. I reloaded for years before I stepped up to my own stuff (Lee 50th anniversary kit). I got a scale and a powder measure (I couldn't get either to work satisfactorily, but some guys love them) and other things I still use today. Most of my stuff is piece by piece as it came along second hand, but my main presses are Lee. Now, Classic Cast, but still Lee.
Enjoy, OP.