regarding the CPU,the E6850 is out of the question, the E6XXX series have been replaced by the E8XXX series.
if you are into overclocking, i would go for the Q6600. many people have been able to overclock theirs to 3gHz, mind you they had to install aftermarket CPU heatsinks.
if you are not into overclocking i recommend the E8400. it is a dual core CPU native @ 3gHz.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115037regarding the 37" tv,this tv might be a little much for a graphics card, i dont know how well any games will look or handle on a screen that large. but if you have it already, it doesnt hurt to try.
If I want to do this what type of motherboard do I need?
depends on your budget and if you want an SLI ready board.
If I want to do this what type of graphics card do I need?
a good one. you will, however, not get a high end graphics card for only $200. i recommend the EVGA 8800 GTS 512mb for $269.99 @ newegg.