Your requirements are contradictory in every respect.
A ruggedized compact sports and active lifestyle camera will not have interchangeable lenses and will have a small sensor, even if you can get good optics.
But that's what I had on me when the "good stuff" gets sealed up in the storm bag, under Niagara Falls. I bought it for my in-laws to use and have a weather-proof (submersible, shock-proof) camera in the party.
I currently use both a mirrorless and a dSLR. Since you are interested in learning to really drive it, I recommend a dSLR. Specifically a APS-C ("crop") body that's cheaper to buy into and lighter than full frame; automatically more tele-photo (what you want) and you are not interested so much in full-frame's specific strength of low-light performance.
New low-end have the image quality of yesterday's mid-grade, but lose features like rapid burst shooting. You want one with two dials, so you can adjust both aperture and shutter easily: if looking low-end, check for that.
Get a major brand that has a mature and common selection of lenses. That is, Canon (EF/EF-S) or Nikon (not familiar with the lens types). You can retain the lenses as you upgrade, find uses lenses, and rent lenses.
For a specific recommendation of something I'm familiar with, look for a used Canon 60D. (When I sold mine, I found lots of them listed on eBay etc. probably for the same reason: upgrades to 70D for better video. So the "used" price is depressed but they are still good cameras. N.B. Michael Clark points out that the weather sealing isn't as good as other choices in the tier.) Future readers: the point is that at any given time there may be some less-than-current model available for an especially low price.
Also important: plan a way to carry it. A strap to keep it from swinging on your chest while hiking, and cover it against splashes and sudden light rain.
When you see something you like, check dpreview for details on how easily the settings can be manipulated and how it performs, as well as weight.