1080p means the vertical resolution is 1080 pixel. The resolution (pixel count) is 1920x1080 for your TV.
The physical size of the screen, be that a 23" monitor or a 42" HDTV is irrelevant. Only the resolution will effect performance.
But moving on, what games do you wish to play? Do you wish to have quality akin to consoles, (medium settings) or do you wish to have most of the eye candy such as on Ultra settings in games?
Which games do you see yourself playing on your HDTV?
Do you need to purchase an operating system? or do you have a copy of Windows 7/8 from a previous PC you can use?
Answer these questions and we can provide a VERY accurate estimate for you, as well as suggest the exact parts, and where to obtain them if you wished to do so.