First, you don't need yellow fever for Zimbabwe. Not sure why it's recommended, but it's not required, unless you're arriving from a country which has yellow fever. Those countries which do require it, generally check to make sure you have it, or they won't let you in. Zim is not one of those. The only reason not to get it, apart from a potentially sore arm, is that only specially licensed facilities can give you the shot. If one is nearby, great, but otherwise, it's more difficult to get than any of the others which even your family doctor or pharmacist could give you. I got it because it is required in Cameroon.
Here are my views (I have all of these, but I've been going to Africa for some time):
1. An up-to-date tetanus booster.
2. Hep A, B and C. You can get A and B in one shot (Twinrix).
3. Typhoid. Not as big a deal now as it once was.
4. Polio. Some recommend a polio booster, even though the shots you received as a child should be enough. I think this is more of an issue in West Africa, where polio is staging a bit of a comeback.
5. Rabies? I got the vaccine a few years ago. I don't really think it's necessary - if you're exposed, you still need to get the shots, but you have more time and don't need as many (or so they say - not one I'd mess with if I was exposed!). The vaccine is a series of three shots, given on a set calendar, so if you want it, you need to plan ahead.
6. Cholera. Dukoral is available, but seems to have limited effectiveness. But given circumstances in Zimbabwe these days, it likely wouldn't hurt, apart from the taste (baking soda).
There are other threads about which drugs to take, but I always take the following:
1. Cipro. Works for travellers diarrhea, as well as being a good broad spectrum antibiotic.
2. Malaria. I use Malarone. I used to use Lariam, but the dreams got to far out.
3. Doxycycline and Levofloxacine. The two together are the standard treatment in South Africa for tick bite fever. Having had it once, I always take these with me.
4. An oral antihistamine and a cortisone cream. Bites can get very itchy, and scraping leads to infections.
5. Ambien. I don't like to waste too much time getting adapted to the time change, so I try to sleep on the planes over (my flights are night flights). Ambien makes that work.
6. An antibiotic cream like polysporin.
And, of course, lots of any medicine you normally take.
Zimbabwe used to have reasonable access to pharmaceuticals in the big cities (Harare and Bulawayo), but these days, I wouldn't count on anything being readily available, and you're likely to be some distance from those places in any event.
Have fun!