Hi Edelweiss,
I have just completed my hunting trip to Africa. And like you twelve months ago I was faced with same dilemma as you. As Mike has stated earlier don't discount buffalo from your list of species. I can promise you buffalo hunting is very exciting and if it is in your means I would seriously consider it.
I split my hunt in two parts and in two different locations. First was a 7 day Buffalo hunt in the Omay South of Zimbabwe. And the second was 7 days plains game in Nicholson West and Beit Bridge in Southern Zimbabwe. My list of plains game was pretty small as my priority was the buff.
The finally tally was 1 Buff, 1 Bushbuck, 1 Eland, 1 Impala. I did also want Kudu but just simply ran out of time.
At least in Zim the best time of the year is a little dependent on what and where you are hunting. For example the area in the Omay I hunted the buff are not that water dependant as there seems to be a lot of natural spring that run all year.
You can pick up some good deals on late season hunts, however be prepared that it will be very hot.
On the topic of what rifles to take, there are about a million threads on the forum discussing the merits of various brands and calibres that guys take on safari. I found that having good optics is a must as you will almost certainly be shooting through some cover (Although not necesserelly far). Second, take whatever you can shoot accurately (Keeping in mind any legal minimum calibres). If you are going to hunt buff, your rifle should have open sights and detachable scope mounts (such EAW or Recknaigles). Warne, Leupold and other QD mounts are simply not suitable as they are to slow and not predictable in maintaining zero when re-attached.
If you are considering hunting Eland, Kudu, Buffalo be in the best physical condition that your age and health will allow. You will be following tracks (hopefully) and on some days that can be a few miles.
I found that the countries to consider hunting are pretty much determined by your budget. Depending on the species and the type of hunting you prefer (fenced game ranch or unfenced concession) will also have bearing on where to go. I stand to be corrected, but when I was doing my research Botswana and Tanzania are probably the most costly. For plains game only I would think Namibia, South Africa, Zimbabwe are good. If you add Buff to the list Zimbabwe would be my choice in affordability.
These are only my personal opinions and I don't proclaim to be an expert. Do your research as all have advised, speak to operators, and also have realistic expectations.
Most importantly enjoy the experience as you will only ever go on one first safari.
