Yea, the 70D will be quite good for you to start with, if you can afford a bit more to step up to it. And the new Tamron 150-600 will be pretty great as a fairly good telephoto zoom. You'll also end up needing a good tripod, most likely, and you don't want to skimp on that.
If you can manage, buy the 70D, Tamron 150-600, good tripod (budget $500-1000, and definitely get Arca-Swiss compatible). Macro, I think the go-to in Canon land is the 100L f/2.8 IS. It'll really bust your budget, but you can always get it later. Or switch and go Macro first, and then get the Tamron later on.
Realistically, you'll have to go over $2K for a fairly good body (meaning one with acceptable AF for the racing photography) plus telephoto lens, plus good tripod since you _will_ need one. Theoretically with enough light you can hand-hold the Tamron with enough light, but while it's not a monster like the 800mm, it still weighs a too much for most people to handhold for very long.
And trust me, don't try to spend $50 for a tripod, it'll suck. You'll end up buying another one for $150 thinking you'll be set. Then you'll go for $300, and it's better, but then you'll just end up spending more money to get something that's quite good. Ah, here's the link, Thom's tripod article
. Look at Maxim #2.