One of the best Kili operators is Adventure Dynamics, which is based in South Africa. They can take you up any route, and can tailor your package to suit you.
The owner (Sean Disney) has summitted Kili about 20 times, in addition to doing the Seven Summits twice, and both Poles.
The local guides used have a good relationship with Adventure Dynamics, and they are well organised and friendly.
I have no hesitation in recommending Adventure Dynamics. I climbed Kili with them in 2012.
Whilst Kili is relatively easy, Adventure Dynamics has an amazing success rate.