All the heps for anywhere these days, yellow fever (though I think it's valid for life, no longer 15 years, and in all my travels no one has ever asked to see my little vaccination certificate). Typhoid, cholera, and diphtheria for anywhere in Africa.
Rabies is only really necessary if you're likely to be exposed to wildlife (rabies vaccine and immunoglobin can be administered if you do get bitten, it'll be available in any tourist centre like Kilimanjaro). Malaria is not a big deal, since the mosquitoes don't like mountaineering, though if you're going to spend time at lower levels it's worth it (I've always used Malarone and haven't got malaria yet despite possessing an irresistible allure for hungry mosquitoes).
It is basically a long hike rather than a climb but as said, don't underestimate the altitude (about 6km above sea level). It how I discovered that as someone bought up in a place where the only hills were courtesy the local collieries that I was never going to become a mountain climber. I don't get on with Diamox either. I'm also banned from Tanzania, for that matter (actually probably not, since I'm on a new passport now).