How much are you willing to spend, i know you're looking for the cheapest way...I don't know if the performance of the card effect tv out...i imagine it does. I have a fx5200 which isn't a good card gaming wise but i've used it for tv out and it works great.
My Rig:
AthlonXP 2000+ 1.677ghz
GeForce Verto FX5200 128mb DDR
Maxtor 7200RPM 80GB, Stock 40gb
Kingston 384MB DDR
Cendyne 52x24x52 CD-RW
Lite-On 4x DVD-RW
Go EMachines...🙁