Preface: I agree with
@rookhawk about set and forget for your double hunting rounds (and maybe your bolt carts) once you've figured out your final loads, but you don't have to do a turret press to make that happen.
This would be my recommendation for someone just starting out, wanting to start with the "big stuff", and not having a real interest in handloading for its own sake, because these are not the qualities of your typical handloader. Handloading isn't for the impatient; it's the fly-tying of big game hunting. Before buying any equipment, buy these three manuals and spend a lot of time reading to understand the principles and processes of handloading.
Lyman has the best guides on the equipment and components you need without selling you anything and the best info on what to watch out for. Graeme's book does this as well, with a deeper focus for large African brass cases. Hornady has load data for all the African cartridges as a backup reference to Graeme's book. This combination of manuals is the best I can think of for what you want to do. Total cost $125
I would start your handloading journey by loading for a pistol cartridge, revolver if you have one; any one will do. This will be a smaller version of your double carts you can get familiar with the process of measuring, charging, seating, etc. The Lyman and Hornady manuals have you covered for any pistol cart you may have.
Press: There's no progressive (auto) press that will handle African carts. Turret presses are fine but I prefer single stage; I have three. I like to keep my dies in their boxes when I'm finished and set them up for each loading session because how I'm loading a particular cart changes from time to time. The other thing is if you ever want to use large body dies, you want a single-stage like the RCBS Rock Chucker Supreme or Redding's Big Boss or Ultramag presses with the included bushing; turret presses can't accomodate them. In any case, you want a press with a frame opening larger than 4-inch; the Rock Chucker is 4.25, Reddings are 4.5 and 4.75, respectively. You could spend $90 on a Lee Challenger 3 that will load anything you want (yes, it will; I have one) up to $1400 for the Area 419 turret that will also. It's personal preference and you may end up with more than one press.
Dies: For the big African carts, I would get RCBS at around $200 each. You don't need to be brand loyal when it comes to dies; I have sets from all the majors and two or three sets per cart. If Lee makes dies for your carts, they are an excellent value and make ammo just as high quality as the expensive dies- mine do. Even when I choose an expensive set for some reason, I always buy the Lee set also. I have at least two sets of dies for all my carts, but I like dies! $35-$250 per set depending on brand and caliber.
Priming: I prefer on-press priming, nothing special needed. I don't mind placing one primer at a time by hand. Personal preference. For hunting, specialist priming is not necessary.
Triming: Yes, you will need to trim for loading consistency, performance, and safety. I would get the Forster hand trimmer because they make a trimmer specifically for large cases. You could do my setup with the Classic on one end for your double carts and Original on the other for everything else. Graeme talks about modifying his Lyman trimmers for large cases; the Forster Classic is ready to go out of the box with correct size collets, pilots and trimmer heads. About $200 for each trimmer in kit form that includes the collets and most of the pilots.
Annealing: You don't HAVE to anneal, but I think there are benefits especially for the larger cases. Graeme thinks annealing is important and describes several methods. It's not difficult and you can practice on cheap cases (like your pistol cases).
Powder dispensing: You can scoop or spoon powder for free or you can buy expensive auto dispensers. I prefer to scoop and trickle with my Lee powder scoops and Lyman trickler, but I recently bought a new Lyman measure and three old 55 measures to play with and they are very good with extruded stick powder- I like the older measures better. I would still throw short and trickle because I want to know that my charges are accurate and consistent.
Powder measuring: I prefer a digital coarse and beam scale final measurement. Again, I believe a manual process would be best for what you're trying to do UNLESS you're willing to spend a grand or more on powder measuring. I put my pan on the digital scale, get close with the scoop, put the pan on the beam and trickle to the balance point. Nothing can be more assuredly accurate than that! I don't need the digital because I know my scoop weights- just personal preference.
Cartridge measuring: I hate measuring case length and OAL but it's necessary. I have dial calipers with the Hornady bullet and headspace comparater sets. I also have a fancy bench mounted, spring loaded dial caliper for headspace/shoulder bump but I never use it. Simpler is better and close enough is close enough in most cases. For me, case length is the most important thing because you don't want the case too long so the mouth jams into the chamber throat. It's also important for bullet seating depth consistency.
Miscellaneous: I use Lyman tumbler and corn media with the polishing compound already added to it. I studied the wet pin tumbling and decided it wasn't for me. Too much extra work loading, dumping, drying, collecting the pins, extra wear on brass. Dry is tried and true. I load black powder cartridge also where wet tumbling would make sense, but even in this case, I just soak in soap water and be done. You need one of those hand tools to chamfer and debur the case mouth; again, I prefer manual to power.
Bench: You can go dedicated, elaborate room with all the trimmings or setup a portable table in the corner of an office. I have a small folding computer table made of half-inch pressboard that is FLIMSY (TV dinner tray shown alongside for scale), but I have no trouble sizing 416 Rem Mag or 45-70 on it. I C-clamp my Co-Ax press to it and go to work. I also put my Lee benchplate mounts on it. It all depends on what you want and need, how you want it to look, how permanent you want it to be, etc. I like my stuff portable and hidden when I'm not using it. I have boxes and cabinets with all my stuff tucked away when not in use. I don't care for stacks and stacks of visible components and tools; other guys prefer it. Personal preference. Good luck (start with the manuals then decide)!
