never particularly understood the fascination with the 50mm focal length as a walk-around shooting lens length. it may be because I started off shooting architecture, but the 50-85 range to me is always, as someone else mentioned, either too-tight or not-tight-enough when I walk around with it. I'd far rather have a 28mm or 35mm prime to use to general purpose photography (focal length on a FF sensor) ...
as far as the OP's gear goes, it's a fine start ... but really any lens and camera at all is fine as long as you learn how to use it properly. if all you had was a 60D and the 200mm f/2.8 prime, people on the forums would all observe that it was a bizarre focal length to start with and go buy other stuff ... but if you have some smashing images shot with a 60D and the 200mm f/2.8 ... who are they to tell you anything?
it's cool to be a generalist photographer, most people who aren't doing it for the money enjoy the freedom to be a generalist (and many working professionals secretly harbor the desire to be a carefree generalist). learn the craft, learn your equipment, and just shoot shoot shoot. people say quantity doesn't count, just quality, but in reality, unless you're freakishly gifted and visionary, quantity counts as well. shoot until the shutter mechanism on the camera breaks, and I guarantee you will see improvement in your work.
I feel quite comfortable as a "generalist", true! But for the future I may leave this status, also because I consider making money with photography (and will have to get these so called zoom lenses).
For the most walk around, I am using, as I stated somewhere above, the 28mm lens as a 44mm equivalent on my 60D crop, and it's just on the edge to be too tight. I agree with you that 50-85mm may be too tight/not too tight. That's also the reason I love it to use my 15mm fisheye on my crop camera, so I got a ultra wide (24mm equivalent), so it compares to the set up with a full frame and a 24mm/35mm!
As well I agree with the quantity shooting! In his amazing book The Passionate Photographer, Steve Simon quotes another guy (I can't recall his name at the moment) from the film age, telling that until you reach 100'000 shoots, you are not a (real) photographer. ;-)