Everything here is background for a conversation with your own doctor, who knows your history. Nobody on a website can tell you what to take.
See a doctor early, not late
Six to eight weeks before you fly, so there's time for vaccinations and for a prescription if you want one. Tell them you'll be sleeping above 4,000 metres and walking to nearly 5,900. That sentence is the one that matters, and a lot of travel clinics will adjust their advice once they hear it.
Diamox, since everyone asks
Acetazolamide, usually called Diamox, is a prescription drug that speeds the body's adjustment to altitude. Lots of climbers take it. It isn't compulsory, it isn't a shortcut, and it doesn't make it safe to ignore symptoms. It has side effects: tingling fingers and toes, needing to pee constantly, and a strange taste to fizzy drinks are the common ones. If you're going to take it, get the prescription at home, and try a dose before the trip so you find out how you react somewhere comfortable.
Vaccinations and malaria
These change, and they depend on where you're coming from and where else you're going, so this is outline only. Yellow fever certificate requirements depend on your route into Tanzania. Routine vaccinations are usually reviewed before a trip like this. Malaria is a lowland risk rather than a mountain one, but you'll be in Moshi or Arusha either side and possibly on safari afterwards. Check the current position with your travel clinic and the WHO travel advice rather than with us.
Conditions that need a proper conversation
Heart and lung conditions, uncontrolled high blood pressure, sickle cell trait, epilepsy, diabetes, recent surgery, pregnancy, and some medications including certain sedatives. None of these automatically rules you out. All of them need a doctor who knows you to weigh in, and your operator needs to be told the outcome.
What to carry yourself
Your own regular medication, in its original packaging, in your daypack rather than your duffel. Painkillers for the altitude headache. Rehydration sachets. Something for an upset stomach, blister plasters, lip balm with sun protection, and very high factor sunscreen, because at 5,000 metres the sun is savage even when the air is freezing.
What the crew carry
A reputable operator carries a first-aid kit, a pulse oximeter and bottled oxygen, and the guides check climbers twice a day. Oxygen is for emergencies and for descent. It isn't there to let someone keep climbing, and any crew offering it that way is doing something dangerous.
Hygiene, unglamorously
The most common illness on the mountain isn't altitude, it's a stomach bug passed around a mess tent. Hand sanitiser before every meal, every time.
Teeth, eyes and the small stuff
A dental problem at 4,000 metres is a long way from a dentist, so get a check-up before a trip like this. Contact lens wearers often struggle with dust and cold and no clean water, and most switch to glasses for the week; bring a spare pair and prescription sunglasses, because the glare above the cloud is genuinely dangerous to unprotected eyes.