As already mentioned, you do not need a TV Tuner card to display a PC on a TV as a monitor. How good the quality and what resolutions you can use will rely solely on the TV at hand... what it supports and what inputs it has.
You mention your TV is a flat screen.. does this mean it's an LCD? HD possibly?
It should at the very least have SVideo and composite input. Svideo and composite will severely limit the resolution and quality of your PC display. Newer TV's also have DVI and/or HD inputs (rca cables again). If your TV has HD input, you're golden as this will support 480/720/1080 resolutions very crisply.
If you're limited to svideo and/or composite, choose svideo and hope for the best. Most svideo/composite cards can provide a semi-okay signal at "useful" desktop resolutions of 640x480 or 800x600. Anything higher is generally beyond the signal quality or scaled.
Most modern videocards come with TV-out, so you should be okay wiith your choice of videocards. ATI also sells AIW AGP videocards reasonably priced at all budget points- so if your TV does support HD-inputs, this would be the best alternative.
720p on a Sony Wega HDTV works great on every ATI AIW I've tried it on. It yields crisp, sharp desktop text and amazing widescreen gaming.