The 70d is great. This lens and flash are also very good without breaking the bank. The first few years of kids you'l be taking alot of pictures indoors, so a fast (low f-stop) lens + flash will work well for you.
70d body: $700 Canon Refurb store Sigma 17-50mm OS $300 - 400 Amazon YN 685 Flash $110 Amazon
If you can get without TTL there are the yongnuo flashes, I've personally tried the yn560iv and the yn685 with their triggers. As for triggers you should use the YN560-TX. All of these must be the Canon versions (not the nikon ones).
With the trigger you can set your flash(es) parameters from it (without touching the flashes themselves) which is a big advantage once you've set the flashes in place, maybe inside a softbox, etc.
Don't buy the yn-622c-tx which, while it works on canon bodies, and it even gives you TTL with the yn685, doesn't even fire the flashes on M43 cameras, at least not on the olympus E-M10 and the Panasonic Gx85.
I've tried all of the above-mentioned yongnuo products on both of these cameras (E-M10 and Gx85), I'll add some amazon links to the products, I hope they can be helpful