Wireless Solution for Fraternity House?

I live in a large fraternity house with about 25 other people. We used to have a single router for the entire house except it did not reach upstairs or downstairs. Also, the single router could not handle the amount of users that tried to use it. I have a little bit of experience setting up wireless networks but I am far from a pro.

The solution I have arrived at is to get a router and two APs. I would put the router on the main floor and put one AP upstairs and one downstairs. We luckily have Ethernet ports on the ceilings, but we do not have power outlets so I would want to use PoE AP's. I know I need a PoE injector to actually deliver power to the ethernet ports, but I'm not positive how that works. We have very good wiring in the house so if I were to put an injector somewhere in our downstairs would I be able to power both the AP's? And also how would I set the network up to switch from the router to the AP when walking upstairs and basically just switch from one to the other when walking through the house?

Thank you for your expertise.