I am looking into buying a PC for Skyrim soon. To save costs, I would like to use my 32" Sony Bravia if there is no reason not to. It only does 720p though, not 1080, would that be a big deal?

It would be best to get a 1080p TV if you can, since it supports more resolutions, but it's up to you. I dual monitor with my TV at 1080p and my computer monitor for gaming,
photo editing, and pretty much anything I can think of. So no there's not any reason not to. Just use an HDMI cable and you're set

It depends on how close you are to the screen. Monitors are designed to show a "per pixel" resolution. My 24" monitor has exactly 1920x1080 pixels. A 1080p TB stretches that over more pixels, causing it to loose sharpness when closer to the screen. Meaning if you use a TV, you will have to sit further back in order to get the best possible picture, as well as save your eyes from the brunt of the damage.