LCD TV vs LCD Monitor for Xbox
Solution 1:
The main difference between a TV and a monitor, besides the TV tuner, is the pixel density. A Full HD-TV has a resolution of 1920x1080, which is similar to common monitors, but spread over a significantly larger area. The consequence of that is that the recommended viewing distance for a TV is much further away than for a monitor.
In short, if you want to sit on a couch and play, get a TV. If you sit on a desk, get a computer monitor.
For a Kinect a relatively large distance to the screen is required, I would recommend a TV for that reason.
Solution 2:
Depends entirely on what distance from the display you will be playing. The general rule of thumb is the further away you play, the larger the display should be to a) avoid eye strain and b) actually benefit from higher resolutions like 1080i or 1080p.
Since the Xbox 360 only outputs a maximum of 1920x1080 (1080p) and assuming you'll be playing say 3-5 metres away from the display, the 32in TV (hopefully one that supports 1080p) would make more sense.
Also, should you decide to invest in Blu-ray the TV will likely support the 24Hz mode needed to handle the pure 24fps Blu-rays can output. Most LCD monitors don't support this output.