My questions to you; do you see yourself improving your photography the past few years and does that matter to you? If "yes," do you want to continue improving? Do you have others praising your photography? Are you interested in printing images bigger than 13x19? If "yes" here's the kicker...If you accidently left your camera at home and realized it once you started your hike/climb, how bummed would you be...scale of 1-10.
I certainly recommend a dslr if you answer yes to most of these questions and here's why. No matter what they say dslr's will never go away. Every pro photographer on this planet is invested in dslr's. Most up and coming photographers are invested in dslr's. And every camera company I know of is primarily dslr driven. If you want to improve, that means you will need a line of cameras that fit your needs at the time you are improving, and in time, you will want choices to migrate to the next level...without reinvesting in a different camera system. Your choices will be limitless for as long as you're alive.
Going mirrorless, YOU will be the one waiting for the next step in technology. The mirrorless system is still in its infant stages and if you believe that the market will grow, then you must have faith everyone else out there feels the same, because if their isn't demand, you may be stuck waiting. I can tell you that waiting sucks. Nikon users waited 4 yrs for Nikon to announce the high res d800. I actually jumped ship to Canon, because I was tired of waiting for more resolution. In a two year span Canon and Nikon release on average 6-8 dslr's, 10-12 lenses, compared to maybe 2 mirrorless cameras and 4 lenses.
I would recommend a mirrorless camera if size and weight matter most and if this system will work for you for the next 4-5 yrs.
At any rate, the above is just my opinion. I've looked at mirrorless myself as a second camera and maybe in time I'll pick one up. For what they are mirrorless has some nice benefits and features.
Back to your question, which camera and lenses to start with. I prefer spending my money on glass first, then finding a body that complements my needs. Remember, “glass is forever and cameras come and go…” In the dslr world, you have so many different options for cameras. Don’t forget that upgrading a camera is easy to do on Craigslist or Ebay as well.
Since you’re considering two different systems that require one to change out lenses, certainly don't be afraid to get two lenses. As USAkeller notes, not having the right focal length will piss you off when you want a certain shot. I recommend the range of 16x300mm with two lenses; the Nikon 16x85vr and the 70-300vr. The difference from 16mm-18mm is a lot more than you may think and worth the price. If you cannot afford the mentioned lenses then go with the 18-55 and the very nice 55-200vr. I’ve owned both the 16-85 and the 70-300 and we’re talking about clean glass that will really improve your photography. I migrated through 3 camera bodies (d200, d90 and d700) while owning these two lenses.
Before I talk about Cameras, understand one thing, high resolution (mp count) will not matter if you do not have clean glass that will deliver the proper lighting and detail to your sensor. Investing in a 24mp camera would be a complete waste of money unless you pick up the 16x85 and 70x300. Matter of fact, you may need some of Nikons $1500.00+ full frame lenses to take advantage of all that resolution. I personally think Nikon is trying to take advantage of the newbies out there with the release of the d3200. 24mp sounds impressive right? Forget it unless you drop some serious money on glass.
I recommend the Nikon d5100. That camera has 16mp which is perfect for the above mentioned glass. The 5100 uses the exact sensor as the award winning “killer” d7000. It also has the 921,000-dot LCD screen which is a way better LCD than the 3100.
These are my recommendations. A d5100, a 16x85vr and 70-300vr will be all you need for years to come. Lastly, never forget about ease to sell and resale value, all of the above will sell in one day over on Craigslist at a fair price. People love Nikon and Cannon.
Hope this helps and let us know what you get!!!