Hunting Africa, unfortunately for the prospective hunter, offers options every bit as diverse as hunting North America. There's everything from Mexican sheep to Canadian Polar Bear, and Africa is no different in range and cost variability. First, is to decide on what type of experience you want, and it seems you know with the plains game hunting singled out. Plains game is some of the most enjoyable hunting in Africa, and I had more fun stalking Gemsbok for days unsuccessfully before finally connecting on a long shot than I did tracking and hunting Lion. Plains game, in a natural habitat, can be incredibly flighty due to conditioning with predators and hunting, and it's a satisfying hunt- depending on the operation. I won a hunt a few years ago, and it was a relatively small area in South Africa (hereafter referred to as RSA), it is what you'll most often encounter on a plains game hunt in RSA. Nice fixed position lodge with all the comforts of home, commercial hunting, good people, great food. Pretty dull in the adventure aspect, and I don't mean this as a negative, it's just the way it is and you know what you're getting into. It could prove a shock to an Africa first timer, however.
Operations like that will literally dart animals to measure their horn growing progress, and analyze their droppings for mineral and feed optimization for growth, I've seen it. One Sable was darted in a place I hunted to ensure the length was known to the mm, as a wealthy Russian wasn't going to travel for anything less than a given size. It is business, and big business, with a touristy feel behind high fences. The fences are often spaced far further apart than large islands in Canada, one fenced area I drove across was 750,000 acres. This said, it can also be the ultimate wind down with friends. My brother and I hunted a luxurious lodge and ate top rate food, taking plains game, drinking the evenings away around a fire with good company, and had a splendid time. It's exactly the same flavour as a top rate wingshooting lodge, stocked game, good food, and very relaxing. The hunting believe it or not often provides enough challenge to be interesting, and you will strike out on some species.
Now, if you're game of heart and after a wide open experience, there is only one place, maybe two, that is affordable at present that I am at all familiar with. There's a third I'm headed to this winter, West Africa (Cameroun / Central African Republic [CAR] etc), and I'll have an opinion on my return. For more conventional Africa with conventional species people picture when you say "Hunt Africa", Zimbabwe and Mozambique spell it out now, in my limited opinion. I haven't been to Mozambique I should point out, but have it on good recommendation and authority from people I trust it is the experience I'm about to describe. Namibia has corners of the experience as well. That experience is open Africa, tent camps, game that may have been poached out, may have moved, unforeseens, tick fever that can wreck a whole hunt, a distinct lack of fences and wilder sorts of people to encounter. You're going to pay more, too, but you're going to come away with more, though likely less heads on the wall. Mine didn't even make it out of the country.
Expect lost luggage on small carriers, including your rifles and ammunition (can't even legally take a rifle to Zimbabwe from Canada, there are all sorts of interesting road blocks), and the potential for illness is far higher, two Americans fell so ill they had to leave the camp where I hunted just before I arrived to hunt Cape Buffalo due to tick fever and lost their chance at Buffalo. A pair of Germans I met had their elephant hunt crashed by corrupt government forces who threatened to arrest them for poaching less their palms were greased, despite having all the proper paperwork. Your PH is likely to have shot poachers, and you may encounter poachers during your hunt in hair raising situations. Depending where you are, you may be handed a .38 revolver before you and your PH go to town. It's a different world, and one I recommend seeing. I have one hunt I have to return to RSA for, as the species literally can't be hunted anywhere else. Beyond that I will only return to visit family, and vineyards with the Mrs.
You can put together a good plains game package for as little as $7000 in RSA, and have a proper time drinking good beverages around a hardwood fire, with engaging company, have fun all day hunting and return from the trip refreshed with a smile on your face. Or, you can spend $20,000-50,000 and get sick, lose some valuable possessions, and have the time of your life that you only properly appreciate after returning home and sleeping it off for a week. You'll have stories you'll actually want to tell your kids when they're old enough, from that one too. Don't get me wrong, there are some genuinely fantastic experiences to be had within RSA with some fantastic operators, just know what you're going there for. The hunting industry is the greenest business on earth, generating income from the natural species of an area, and I support it wholeheartedly RSA and elsewhere. It is big industry in RSA and can feel like it however, and as you pass large commercial maize farms and cattle ranches on the way to your farm, and it is quite honestly typically referred to as the "farm" by the PHs, pass through the gates of the electric fence, and settle into your air conditioned cabin with carefully grass thatched roof, the charm can be lost to those who've seen places like Northern Canada.
My advice is to save to do the trip right, and do one good trip rather than a few not bad ones- this does not mean don't go to RSA expressly. If you're looking for a vacation, with some excellent trophies, some excellent food, and to make some new friends across the pond RSA can be fantastic! I can certainly see the charm of RSA comfortable operations with two young kids, a job that has me deep in the bush most of the time in camp, a lot less personal time than I could wish, and enough first world problems to create a little stress. In light of that cheersing Castle lagers around a stone hearth under a blanket of African stars with my brother, knowing tomorrow we'll have a good sporting day of hunting, is a hell of a fine way to spend some time. You will come home missing something, however, and feeling a little too healthy.