Steve's list is fairly concise but I would add a few to his list:
1. Lug bolt torque...should be 100-110nm
2. Wheel bolts, if different from stock, should be checked for proper flange seat diameter
3. Wheel runout...look for the obvious, ie, a bent wheel.
4. Rotor runout....measured cold
5. Hub/bearing runout......mesured hot
6. Suspension damage or wear.
- tire runout (side to side)
- tire round
- wheel round
If it's ONLY under braking, I suspect warped rotors 90% of the time. Then move on to the others, starting with hub/bearing runout.
Why does it only happen at certain speeds? Because vibrations are strongest when they hit a certain resonant frequency. In this case, the wheel vibration matching the resonant frequency of the rest of the car / suspension. Typically, this is usually around 60mph. The fact that it's 70mph in this case could be due to the stiffer suspension.