The great thing about the G6 and other M4/3 camera's is that you can adapt any lens mount you want.
I have a Mamiya Sekor lens set and a Canon FD lens set.
If you want to keep it simple, just buy a $10 adapter on ebay for your lens mount to M4/3.
If you have a little more budget, invest in a focal reducer/speedbooster clone for approx. $100. This will help with the crop factor on M4/3 and low light shooting.
Don't buy a 85 as a first lens on M4/3. This will give you a 170mm equivalent focal length. Impossible to shoot decent footage with handheld or even with a good shoulder rig.
If I have to suggest one lens to start with, get a manual 35 f/2 or a 50 f/1.4 or f/1.8. You can shoot most of the stuff with that, use the ETC/sensor crop function on the G6 for teleshots with the same lens. Expand your lens set from there over time. If you can, stay with the same lens mount and lens type, that way you'll be sure shots from different lenses match.
Remember that your lenses will last longer than your camera. My Canon FD's are over 40 years old, still in mint condition and will very probably last me the rest of my life. It took me about 2 years to assemble my set, taking my time to look for bargains. My set consists of a 24 2.8, 35 2.0, 35-70 4.0, 50 1.4, 85 1.8 and 135 2.5 and cost me less than $800.