There a few basic types of mp3 players, smaller flash based ones usually sell for less than $100 and will hold 30 or so songs, they are great for joggers, or other exercise activities because they have fewer moving parts. This one has a stopwatch and a fm tuner included
http://www.newegg.com/Product/Product.a ... 6855102171
Next are the hard drive based ones, they can hold a *ton* of music, and are consequently usually a little bit larger and heavier. This one is one of my favorites as far as bang for buck
http://www.newegg.com/Product/Product.a ... 6855102206
It also has a fm transmitter. This is what the original Apple Ipods were. Most of these are around $200 or less, depending on how large a hard drive you get.
The latest is the large flash based unit like the new Ipod Nano
http://www.newegg.com/Product/Product.a ... 6855101432
It is a combination of small size, and larger capacity, various models also include the ability to watch video.
It really depends on how she intends to use it. There are accessories for all of these that allow one to plug them into your car and listen to audio books, etc.
As far getting your music into one, yes, you can "rip" a CD onto the unit, and/or you can subscribe to one of the music services, Itunes, Napster, Yahoo music, etc.