You need to chose your glass and stick with that. If you go Canon, you are going to start building a EF lens set. If you go G6, you're going to build a MFT set. It's almost like getting married!
My suggestion: Go with Canon 60d or T2i/3i/4i/5i or 7d. Get whatever you can find cheap, they are all the same visually. Still photos on all these Canon cameras are superb. In fact, to really save money, see if your uncle has a Canon camera you can borrow for a few months.
Instead, spend your $800 on getting some good glass. I'd suggest the Sigma 18-50 f1.8 EF. That's gives you a great range on any of the 1.6x crop Canon cameras.
Eventually, when you save up some money, you can upgrade to something like the BMCC or BMPCC or GH3 and get a EF-MFT speedbooster and you'll continue to use the Sigma 18-50.
If I were doing it again, that's how I'd play it right now.