I suggest you look at the, right at your budget, Specialized Secteur Expert Disc
http://www.specialized.com/us/en/bikes/road/secteur/secteur-expert-disc

Rear cassette is 12-30 so it is geared down pretty low for the steep stuff.

My Specialized Roubaix has the same frame geometry and the same fork. I love it.
It is a bit more upright than a race geometry road bike but gives you many more riding and hand positions than a flat bar bike.