Honestly go straight for the 400mm f/2.8. Get the MK II version if you can as it's lighter and sharper than the MK I version.
Between that and the 70-200mm f/2.8 lens your going to capture everything you need.
The other two lenses are stellar in what they will be able to do but with the 400 you will be able to get everything you want and more (even if you throw a 1.4 extender on it).
It gets you this....
and this....
and even indoors this...
Oh and by the way the 200mm f/1.8 with a 1.4 extender can get you this...
Outstanding photos, Ross! Thanks. I'm getting all kinds of advice with no real consensus. It's a very tough choice since I don't have the money to get all the lenses!
I think the real issue with me, other than money, is that the 400/2.8 is 12 lbs whereas the 300/2.8 and 200/1.8 are only 6 lbs. AND I'd be more likely to hike around town with the latter two. Given the weight, I'd only use the 400 for sports, but I could use the other two for other things as well. It's quite the dilemma!
You said that the 400 would give me everything that the 300 or 200 would, and more. What did you mean by that?
And is the 400 Mk II really that much better than the first version? I saw a version 1 in the low $2K range, but the Mk II is killer-expensive.