1. Mount Stanley (Margherita Peak) 5109m
2. Mount Speke (Victorio Emanuele Peak) 4890m
3. Mount Baker (Edward Peak) 4843m
4. Mount Emin (Umberto Peak) 4798m
5. Mount Gessi (Iolanda Peak) 4715m
6. Mount Luigi di Savoia (Sella Peak) 4627m
7. Humphreys Group (Humphreys Peak) 4578m
8. Portal Peaks (Kihuma Peak) 4391m
Treks to these mountains can take 1-3 weeks or longer depending on the itinerary you pick, your speed, and the weather conditions. You can work with either company to tailor make an itineary suitable for your wishes and ability. These peaks can be pretty difficult, some include light rock climbing, scrambling, and even glacier crossings.
I have done three treks with RTS each of 8-10 days and summitted most of these peaks. They provide huts each night, beds, matresses and all the food and water you'll need. They also provide basic climbing equipment. Whatever company you go with, you'll get a packing list from them. RTS recently installed wood burning stoves in their mess huts above 4000m, a very nice touch. For experienced mountaineers and trekkers, traveling with RTS is pretty cush, but you're paying for it. You really don't have a choice, so you might as well enjoy it.
While I would rather not publish preference for one company over another, I simply cannot recommend RMS to anyone. I have had many friends use them and come back with close calls, disappoinment, lack of food, and general frustration. On the other hand, RTS does a very admirable job and improves each year. You can read similar reviews online for yourself to corroborate what I'm saying here.
I have tried, as have others, to get access to this park without dependence on a trekking company. UWA simply does not allow this. I have never heard of anyone trekking in these mountains on their own, which is a real shame because it would be incredible! Look on the bright side, you'll be well looked after and free to fully enjoy these amazing mountains.
For this trail, you start and finish in Kilembe. I have marked the points by hand as I did not have a gpx file. RTS has created a loop so you'll follow a slightly different trail on the way out after passing Bugata Camp. Much more info available by contacting them directly.