Consider to "float" that budget upward. A medium size room is considered 1,500 to 3,000 cu. ft., while a large size room is considered 3,000 to 5,000 cu.ft. These volumes (and any rooms open to your listening room) are subwoofer related volumes. Speakers are listening position related (how far away from the speakers do you sit?).
I would also begin with a 2.1 system first (main speakers and sub). Then add the center channel when funds are available, then the surrounds (rears).
I would also begin with a 2.1 system first (main speakers and sub). Then add the center channel when funds are available, then the surrounds (rears).