Actually, unless you are going to be shooting professionally, I'd probably go with the new 70D right now, instead of the four year old 7D (and I use two 7Ds personally).
If you can live without f2.8, you might want to consider the 70-200/4 IS, so that you can get the IS. Yes, with sports sometimes IS is not necessary... But, having used a bunch of IS lenses for sports shooting for over ten years now, I can tell you for certain I have gotten a lot of shots thanks to IS, that I wouldn't have at all, or wouldn't have been as good without it.
I never shut off IS (on two 28-135s, 70-200/4 IS, 70-200/2.8 IS, 300/4 IS, 300/2.8 IS, 500/4 IS) and I don't believe it effects AF at all. Of course I use Back Button Focusing with AI Servo most of the time, so my subject is usually in focus and being tracked long before I trip the shutter. The only thing I ever noticed turning off IS is slightly better battery life (not enough to make much difference... I just carry extra batteries).
A few of my lenses need IS shut off manually, if they are locked down on a tripod. However, they are the type of lenses that I'd rarely put on a tripod anyway... and even when I use a tripod it's usually with a gimbal mount and loose panning axis to be able to track subjects, in which case there is no need to turn off IS on any lens.
The 70-200/4 IS is the second sharpest of Canon's 70-200s. The first is the 70-200/2.8 IS Mark II that costs a whole lot more. The third sharpest is the 70-200/2.8 IS "Mark I" or the 70-200/4 non-IS (they are about the same). And the least sharp of the five Canons is the 70-200/2.8 non-IS.
My 70-200s are my most used lenses shooting sports. Second most used is my 300/4. For motorsports I sometimes use a 1.4X on it, but can't remember the last time I did that for field sports. But I usually have sideline access for any sort of sports.
On rare occasions I've used a good 1.4X on a 70-200 and it's image quality is pretty good, but the TC does slow AF a bit. I will not use a 2X on 70-200... there's just too much loss of image quality.
For general use, you also might want something wider. With either 7D or 70D, you should be able to get it "in kit" with 18-135 IS STM, which seems to be a pretty good lens.
Even better is the 15-85 IS USM (wider for those landscape shots, plus better AF drive, unless you plan to shoot a lot of video), but it's more expensive and rarely bundled in kit with the cameras.
Or, if you want really wide for landscapes, the Canon EF-S 10-22mm USM is a top choice for use on crop cameras.
Between the 10-22 and 70-200, there would be a pretty big gap in the middle, at some important focal lengths. The best zoom to plug that hole is the EF-S 17-55/2.8 IS. However it's also the most expensive.
A three zoom set: 10-22, 17-55 and 70-200, would be a nice setup... add a 1.4X for more reach at times.
If wide enough, a two zoom set with 15-85 and 70-200 + 1/4X would be pretty nice, except there's no "fast" lens for low light... so might want to add some fast primes such as 28/1.8, Sigma 30/1.4, 35/2, 50/1.4, 85/1.8.
On a crop camera, a 50mm is a "short portrait" lens... nice for indoors when working space is tight. 85mm is a "long portrait", good outdoors or any time you have space, and a bit more of a "candid" lens, aallowing you to work a little farther from your subject.
If you want a macro, that's possible, too... and might take the place of one of the primes. I'm currently trying out the Tamron 60/2.0, which thanks to it's unusually large aperture, makes for a nice portrait lens, too. It doesn't have really fast AF, though, so isn't much of a sports lens (it's rather short for sports, anyway).
Really there are lots of ways to put together a lens kit... and I'd consider that first, camera later. Lenses make more difference to your images, than the camera they are used upon.