It think you are pretty much set with the 7D and the 70-200 for the sports stuff. So that leaves you with the question what else you're going to do with the camera.
Lot's of advice here based on people's own preferences but I'm not clear yet what your other use may look like. Do you have a need for wide angle (such as architecture, landscape, etc)? Do you have any use for fast lenses (and to me that means control over depth of field and not so much being able to make pictures in the dark...)? Will you try to shoot portraits and if so what is your preferred focal length for that? Again, how important is good "bokeh" for you? Is weight and size a concern? Do you want to get into flash photography or not at all?
So in other words I'd be very careful with some of the blanket statements here about what constitutes "general purpose" use. Everyone has a very different view of that I suppose. And some of this is always a compromise - especially with the limitations of a cropped sensor if you answered "yes" to any of the questions above...
I personally would always go with the fastest lens I could afford in the desired focal range. But that's me and may be completely irrelevant for your preferences.
and to the discussion of EF-S vs EF and trading... I think that maybe specially people who don't make much money from photography do it as a hobby and then don't look at lenses as an "investment" and if you can have the right lens for a few years and lose $100 in the mean time, isn't it worth it? you couldn't even rent it for a long time for that money... so If you want investment buy... I don't know, Canon shares before you send them money for the lens but that is a discussion for some other forum, I just think that its like buying big all terrain tires for your roadster, because you might buy an SUV in future
btw, other options... you mentioned landscape, probably no need for a very fast lens there, but you might want wide...portraits, if I may, I would suggest the 50mm f/1.8 (an equivalent of 80mm on FF, not a bad FL, good price and it would work on FF as well )...
Of course, and despite what the naysayers here might say, you *can* shoot sports with a 6D. It is certainly not be the best tool for the job, but for anything other than situations where you need to shoot 6-8 fps, its IQ kills the 7D and beats the 5D2, IMMHO+1
and out of curiosity... the sports you will cover, you mentioned football and baseball, so I'm thinking outdoors, but are they mostly held midday, or also evenings, if so, are they well or poorly lit? In other words, would you need to up the ISO and with that, do you care about a discussion "more cross type AF points vs higher ISOs / 7D vs 6D" for example?