I was able to find that people report it has a 300w power supply, which is pretty limiting these days, but quite a few people reported adding a video card with a new PSU so it apparently does have at least one pci-e slot. What do you want to be able to do on your new card, and how much were you looking to spend?
eMachines uses some sorry PSUs, so replacing it is a good idea. I see it is a normal ATX size.
There are a lot of possible choices, but let's just keep this simple. Get a 380W Antec Earthwatts PSU. That can handle up to a HD5770 without problems. They are widely available, whether online or down at your local Best Buy. If the Antec isn't there, do NOT buy a Best Buy house brand PSU (Dynex or Huntkey / Rocketfish), but I believe they also sell Corsair; the 400-CX is sufficient. Then, choosing the graphics card will depend on what you want to do with this PC. The HD5770 or HD5750 would be fine if you intend to play a lot of 3D games. For casual games (e.g. Zynga, online card games, etc) or movies, a HD5450 or HD4350 would be sufficient. There are more choices in between, so let us know what you want to do to get the most relevant recommendations.