Of course you can use your monitor, that's the great thing about it. VGA is a standard connection and as long as everything matches, there's no problem. By things matching, I mean resolution, frequency, etc. The 360 will output 1280x720 @ 60Hz. Pretty much any decent monitor can hande that. Most can also handle 1080i. It will be widescreen don't forget, so you will get borders, unless your LCD is a widescreen model.
VGA switcboxes are available pretty cheaply. Electronic/Computer shops usually carry them.