Where can I find a list of all reputable companies that have music to download,
legally, onto an IPod. 
And how can I find out how the companies are rated for safety. I am
nervous about bringing dangerous ads,spam or viruses, etc. onto my
computer.
Thank you!

Just use the Apple Music Store, which is accessible through iTunes.

The only online music store you can use with the iPod is Apple's own
iTunes music store (subject to it being available in your country).
This is because the iTunes Music Store allows you to buy Protected AAC
files which will work with the iPod, whereas every other legal online
music store uses Microsoft's Protected WMA files which the iPod is
programmed not to be compatible with.

This isn't too much of a problem as the iTunes music store is very
competitive on price and has better usage rights than most of the
other stores.

The other alternative is just to buy the normal cd's then burn them
onto your computer and then upload them to your iPod!

With a legitimate service such as iTunes you can be sure you won't be
downloading viruses or spyware etc with the files which solves your
other issue.

(Obviously I am unable to guide you to illegal sites and services to find music)