Similar-ish situation. I've been multi-day hiking and walking mountains for years, but I'm done with getting cut off from a lot of my favourite routes for more than half the year and want to have more options in terms of routes because a lot of the routes around me are alpine to sub-alpine.
I'm not sure I can give the best advise as it sounds like our targets are quite different. I'm interested in doing alpine climbing, glassier traversal and winter climbs in remote areas. I believe Kilimanjaro is a totally non-technical climb on well formed paths with huts and campsites. I don't think you need mountaineering skills to do it.
I've done some simple non-technical day climbs on my own and I rented gear. After a few months of reading up and with a rough idea what I needed, I just went to a place and told them what I was doing and they gave me stuff (helmet, crampons, ice axe).
The problem were I live, unless you get very lucky, all the mountaineering is technical and most of it is very remote. So I signed up to an alpine course which covers rope work, snow and ice climbing, crevasses, survival etc.
>all my trousers are jeans and I don't like the smell of the waterproof spray
I'd recommend getting a bit more experience in doing multi-day trails before going onto ice and snow, if that's what you want to do. You'll need the fitness and cardio because walking on snow and ice takes a lot more energy that dry ground. You'll also have to keep going for days and learn to be better at packing because you need to carry more gear.
For trousers, I use a merino base layer, padded soft shell and hard shell with gaters. Then drop 1-2 layers depending on conditions. I'll also take a pair of pertex trousers, just in case.