You can do an online search for linux hardware compatibility list, check out the linux documentation project (ldp), and then try various distributions.
To see what is trivial to set up, get a knoppix cd and boot from the cd. It won't install anything (it runs from the cd) and it should be obvious what auto-detects, what needs configuring manually, and what flat-out doesn't work. If you have fairly generic hardware that isn't brand new cutting edge, then there should be at least beta driver support included in most linux distributions. Most HP printers have drivers, most sound cards have drivers, and most video cards even have fairly recent 3D graphics support. CD burning is usually offered as an optional package in many linux distributions, as are image manipulation and sound utilities.
I'd try ubuntu for your first full installation though. It's pretty complete and has pretty good hardware support. It installs with a default Africa global mankind hug sort of theme that I find unattractive, but that's easy to change after installation.
It shouldn't actually harm your computer unless you force certain video settings that are normally not allowed, in which case you could potentially damage your monitor. It's also theoretically possible to destroy your hard drive or at least make it very difficult to make usable again, but again you'd have to force certain settings that aren't typically allowable. It's been a long time since I've read about a linux user catching their monitor on fire or wrecking the hidden boot and firmware sections of their hard drive
I'd say go ahead, but give the "live cd" versions like knoppix a try first. I think the standard ubuntu cd will also boot as a live image without installing so you can try it out before installing anything to your hard drive. Just realize that running the live cd versions will be a lot slower and less responsive than if you installed it on the hard drive.
