Realistically, you need at least 3 routers/access points to accomplish your goal - one per floor. The signal strength from omnidirectional antennas forms a donut, not a sphere. That is, they have great range to the sides, but very short range up and down. High gain antennas are even worse - they increase horizontal strength at the cost of vertical. So putting one router on the 2nd floor won't work as well as you'd expect.
http://www.mpantenna.com/omnidirectional-antenna-radiation-patterns/
You *might* be able to do it with a single hemispherical antenna in the middle of the 1st floor facing up (or 3rd floor facing down). But given the size your house, I have to think the Wattage the router can put out simply won't be enough for complete coverage.
The 150+ Mbps requirement is also a problem, as only the highest-end (wide band) 802.11n on 2.4 GHz can achieve that. 5 GHz 802.11ac can easily hit faster speeds, but being 5 GHz it won't travel as well through walls, so the extremities of your house won't be as well covered or won't be covered at all.
Basically you'll need to throw a lot more money at this problem, or learn to live with much smaller coverage.