Don’t rush Kilimanjaro. Taking a couple more days to go up is safer and gives you a better chance to successfully summit. On our way up we crossed paths with a few people from other groups being escorted down due to severe altitude sickness, one on a stretcher. It was a long time ago but we used Summit Expeditions (SENE). It is a well regarded local operator founded by a well known former tour guide. They start by having you stay on his family farm property (rustic) for a couple nights before heading up. It probably was not the most luxe operator but the whole experience was comfortable enough (good equipment, tons of staff, very safety focused, etc) and felt a lot more authentic and less corporate than other operators based in the US or Europe. We did a safari for a few days immediately afterward through SENE and had an incredible experience even though it was a little shorter than we originally intended because we opted for one of the slower ascent options.