I want to begin sending a voice sample for voice over out with my pic/resume, but I have never made made one before.
I was thinking of reading a piece from a book or maybe a monologue, but I don't know what they want. Am I supposed to do "character voices" or just my normal speaking voice?

http://voice123.com/ check here for some samples.

Do I really have to pay for a professional recording? I was thinking I could just record myself at home and then burn it onto a disk.

No--those were just samples so you could see what you're competition is doing. Plenty of people have home studios.

Ohh, ok. Would I need to add the background music or noise like they did, and if so how? OR... do agents not care?

Agents will throw out a reel that's not professionally done.

Check out the Everything Acting Podcast and the Voices.com podcast for a little guidance.