I did not read the entire post. But I read some of it and checked out the links.
I wouldn't buy a directional antenna unless you plan to point it DIRECTLY at the coverage area. I would go personally with a wide angle.
Unless you are going for a point to point or multiple points. I would go with a Omni-Directional antenna.
for more information on kinds of antennas.
For another router to act as another... You may
need a bridge depending on your plan of connection.
You need a cheap one... Ah.. Lets see..
I looked around newegg.com a little and I see this is pretty nice for the price.
It is 44.99, Free shipping, removable antenna's (three of them).
There is also a special discount going on until 6/30 for that router for special gain antennas making the top price 54.98.