I have never really played Minecraft, because I suck at translating my mental vision into concrete 2D or 3D constructs, but it looks cool as hell, and what I read on the top two sites from my search looked very simple and easy to apply.

http://www.skydaz.com/

and

http://www.minecraftforum.net/topic/1786738-minecraft-mod-installer/

I'm fairly certain the communities there could answer any remaining questions you may have, if nobody here does. Also, definitely post this again in the Gaming forum here if you are still uncertain.

Good luck!

you want to do manual mods, or you can use something like forge, or others, which are mod loaders.

The good thing about minecraft is if you screw up, you can just uninstall the modloader and reinstall it. Like setting it back to "factory default". Don't be afraid to try.

Minecraft forums are fantastic, you'll find lots of help, and there's video walkthroughs for almost anything.

I only use one mod, Rei's minimap.
I highly suggest it. Just pay very close attention to which versions of mods you're trying to use to make sure they're compatible with the version of minecraft you're playing. Also, if you install an update for minecraft there's not always an updated version for the mods also, because all mods are made independently.

It's my parent's computer, and my mom keeps medical billing files and stuff on it. I'm concerned about causing some kind of data-loss disaster.

We dodged that, barely, a couple of years ago when the old computer began acting funny. They bought a new one, so I just took the hard drive from the old computer and used a kit to plug it into the USB of the new one. I copied over all of the critical files, then a week or so later the hard drive toasted.

I just don't want to install a "mod" that turns out to be destructive or steals identity information or something. :-/

I can scrounge up some links, bit it'll have to wait til tonight. I'm at work currently.