By summer we are in a 2700sq ft house with a detached 3 car garage. By winter in a 1200sq ft condo with no garage. So I know both ends of the spectrum. Summer is a three tier 20 gallon capacity brew sculpture, lots of fermenters and kegs, a spare fridge and kegorator. Winter is one bucket, 2 kegs and a jockey box doing kits only.
Your cooler on it's side with frozen bottles is a great idea. I know because I did the same thing a long time ago Hey, your probably going to have a cooler anyway. Didn't come up with the idea myself though.
Kegging won't take up as much room as you might think. Since they are tall and thin the footprint is small and if you are careful they can be stacked when not in use. The problem is when serving. Now you need a kegorator or something. I use a the jockey box at the condo. Google it for lots of ideas. Keeping it full of ice is kind of a PIA but it takes up only the room a cooler does.