1366 x 768 is an extremely low resolution, and TVs usually have low response rates.
(Yes, your 550ti would handle it)
Are you getting this tv off of a friend for REALLY cheap, or what's the deal?
performance should be somewhere between 1280x800 and 1680x1050. it's doable in most cases at 1366x768, but at 1080p, you'll either have to lower the graphics settings or get a new GPU.
if your friend hasn't connect the tv to a pc, i highly suggest you try it out first. using a tv as a pc monitor can be a big gamble on whether or not it'll work to your liking. some common problems includes input lag, ghosting, and poor 4:4:4 chroma subsampling resulting in poor image quality