Time Machine is the application used for backing up, it sounds like you are talking about Time Capsule which is a router that has a hard disk enclosed in the same casing. Time Capsule can be connected wirelessly, most prefer it that way for the convenience and lack of wires.
If you are looking to use an external HD as a Time Machine backup drive they should not be connected wirelessly, they should be physically connected via USB, Firewire or Firewire 800 to your iMac. IMHO it is not wise to scrimp on backup drives, it's your backup so if when they die you've lost your backup! My recommendation is to invest a little and buy quality products that will last longer. What I normally recommend is either:
G-Tech G Series
Lacie Quadra D2 Series
OWC (www.macsales.com) Mercury Elite Pro Series
All are top quality build quality, have similar features and just work well out of the box. Personally I have Lacie's (4 of them) however I wouldn't hesitate buying any of the above.
Roger