See following review for some benchmarks. A resolution of 1366x768 would be in between 1024x768 and 1280x1024 resolutions so you can add the FPS of both resolutions then divide by 2 to get a rough estimate.http://www.techpowerup.com/reviews/Powercolor/HD_6870_PCS_Plus_Plus/6.html
A Radeon HD 6850 should suffice.
Of course, if you plan on buying a 1080p HDTV in the near future, then buying a more powerful card would be a good idea like the Radeon HD 6870 or something faster like Radeon HD 6950 or GeForce GTX 470. It all depends on your budget and future upgrades (if any).