Hi there. I'm a single female who has lived in Kigali for two years. You can trust the taxis here. Most taxis in town are unmarked private vehicles, but not once have I ever had a bad experience with them - nor have I heard of anyone else having troubles. Only the special airport taxis are at the airport. The drivers will be at the door when you walk out the building. With them there are standard prices depending on where in the city you're heading to - slightly higher than other taxis but they really are set prices - they're not ripping you off! I live in Kimihurura, which is a bit before town center, and the price there is 7000 RWF.
On a more general note, there is also one metered taxi service available in town... again this is reliable but I never take it because it's far more expensive than other options.