You'll have to be careful that you're not doing a lot of expensive wheel re-inventing here - or perhaps you don't care and are just doing this for the fun of it which is also fine.
There are a lot of RFID products on the market, you can google for the manufacturers. The power for the ID device comes from the reader, there are a couple of different standards but the most common one works at 125kHz or thereabouts. Have a look for HITAG 1 and HITAG 2, TEMIC, MIFARE, these are all available technologies for ID devices and readers.
If you have "limitless power" ie you make your reader mains powered then you can transmit all the time and wait until an ID device comes into range. Alternatively you can use some sort of proximity detection device to see when something moves close to the reader and only then start reading. Short range passive infra red detectors are being used for this in some products on the market.
On your house you are probably going to install a "fail secure" electric lock of some kind so that your house isn't open if there's a power outage. So you do need to still have your old key or something similar to let you in under these circumstances....or of course if the electronics fails you still need to get in, but hey, that'll NEVER happen.... :wink:
Really, there are a million products on the market that do what you're looking at doing and they cost next to nothing so if you're doing this as a hobby project then fine but if you're doing it for more commercial reasons then I'd do a little research first before you spend any time or money.