Below some tips, including debunking some urban legends regarding a safari to East Africa.
Don't bring a safari outfit. You will be sitting in an air-conditioned car when driving through the parks, and, contrary to what you might expect from watching "Out of Africa", you will not be hacking your way through the jungle yourself. Furthermore, the animals really don't care what you wear, so why would you? Just bring easy-going light clothes with you, and avoid too many white colors because of the dust.
Uganda is safe. Uganda is known as "Africa for beginners" and is surprisingly safe. Granted, there were some rebel activities in the North, but these were clinically kept away from the rest of Uganda and constituted just a handful of rebels that the Government tolerated for whatever reasons. In any case, the rebels have been flushed out under international pressure and the whole country is very safe. Don't believe the overly cautious warnings on embassy's websites!
Don't show up with long dresses or pants. Often, a hilarious scene in Uganda is the army of voluntourism folks that wear long dresses and pants. They do so "not to offend the local population". Wake up - it's the 21st century, and you are actually more offending the Ugandans with your weird outfits than if you would show up in miniskirts!
You will not get sick. The chances of getting sick in Uganda are much lower than in Latin America, West Africa and North Africa. A lot of this has to do with the relatively cool temperature and high altitude. Obviously, you will be armed against malaria, so no worries about that one either (if you don't take malaria prophylaxis: don't come to Uganda).
It is not warm and humid. As mentioned above, Uganda is on average at an altitude of 1,200 m above sea level. This means that the weather is a pleasant 22 degrees celsius year-round, and a tad on the cold side at night.
Please do come during rainy season. Rains in Uganda really mean a large thunderstorm or two during the day, and bright sunshine for the remainder of the day. Furthermore, these thunderstorms are truly superb to watch and also mean less tourists and cheaper prices. All beneficial!
You do not need a visa in advance. Repeat: you do not need a visa in advance! Visas are easily obtainable upon entry in a 5-second deal. Whatever embassies advise you: they are lying (because they want to keep your visa money in-house).