Evaluate what you really want from a setup. I had a full-blown SLR setup with Canon L glass and when I sat down and compared the output from a Sony RX100 Mk II vs my T2i with a 24-70L on it (about a $2000 camera/glass combo) the Sony won in every way and it fit in my pocket. It's a point and shoot camera that can shoot ISO 3200 F1.8 clean. Absolutely ridiculous and I've captured shots with it that I never would have gotten with my full SLR setup because I wouldn't have it with me. And if you are okay shooting JPG (I usually don't), you can use multi-frame noise reduction which lets you capture virtually noiseless images up to ISO 6400.
Is it a replacement for a full-frame camera? No. Is it a complete SLR replacement? No, it doesn't excel at telephoto or macro shots. Is it good enough where professionals in the photo AND video industry use it for studio shots and as a B camera for professional video shoots? Yup.
I have a 12x40 HANDHELD panorama I shot with it in nightime conditions and people think it was shot with a big money setup.
https://dl.dropboxusercontent.com/u/...%20%284%29.jpg (This is actually barely processed, it was blue hour. Adjusted the levels a bit and added some smoothing.)
The video from the Sony will require at LEAST a 3k investment from a SLR to be as good. The optical stabilization is incredible and you will need a big-money, bulky stabilizer setup on a SLR to equal it. Take a look at the video comparison around the web, here's a good example starting a bit over 2 minutes. Keep in mind that's with the old RX100 and the new one is about 1/2 stop better.
To me, for what you want to do get a RX100 Mk ii. Learn to use it to the fullest capabilities of it and then get a 5D MK III. Between those two you have a complete setup. The RX100 just makes any SLR less than a top of the line full-frame seem pointless to me unless you're going to be doing super-wide or telephoto shooting.