Won't someone just tell her something about an MP3 player??? OK, then I will. A little background: MP3 is a compression format. A song on a CD is relatively quite big, being about 10 megabytes per minute of music. MP3 compresses this by a factor of 10 or so. This not only makes it easier to store as far as memory requirement, but much easier to transfer, especially over the internet, which is usually the worst bottleneck. MP3 allows different bitrates, the higher number being the better quality, yet bigger music file. The lowest, (also most common) bit rate that still has quite good music quality is 128,000 bits per second. There are also 160, 192, 256, and 320 thousand bit per second rates. To simplify this a little, call it about a minute of music per megabyte (mega = million) at that standard 128k (k = kilo = thousand) bit rate. So (for example) a song is often 2 to 5 minutes or 2 to 5 megabytes big.
Of course, one of the first considerations is how much memory the player has. A gigabyte is 1,000 (actually 1,024) megabytes and these players come in 1/2, 1, 2, 4, 8, and, lately, 16 giabyte sizes. They also come with mechanical hard drives (instead of memory) with relatively huge sizes like 40 gigabytes, but then you have to worry (more) about what happens when you drop the player and the price, of cours, is stiffer. Probably the best place in the price vs memory curve right now is 4 gigabytes. That would allow for, say, about 65 hours of music at that 128 bit rate, or say, 1200 to 1400 songs.
After that it's a matter of features. Do you live in a place where an FM radio would be useful? Remember that it probably uses the earphone as an antenna, and in any case, it won't be all that sensitive as far as reception. Do you need or even want it to be able to record things? Little details, like can it record from its radio? Do you care if the LCD display is color? Some of these players can actually play movies! Do you want that? Movie format is often MP4, by the way, another compression format. There are other audio (and video) formats, like AVI, DIVX, WAV (not even compressed at all), WMA (Windows format for audio and video), OGG, and some more unusual ones. Can the player you're looking at do any other formats than just MP3? Do you want it to? My recommendation, especially in your case where you probably can't even answer that question, is to go for one that can do as many formats as possible. Some of them have some very exotic features, like electronically flipping the screen so it can be held upside down, a built in graphic equalizer, base boosters, all kinds of settings, and too many other things to list.
Then there's ease of use. Are the controls (buttons) intuitive and easy to learn or are they more confusing than anything else? One feature I would insist on is a lock function; that is, a switch that will make the player stop responding when the buttons are pressed. This keeps the music playing even if buttons are accidentally or unintentionally pressed while running through the mall with a purse banging against the player with every step.
The battery and how it charges should be a big consideration. These things, like most other devices, can use anything between AAA batteries, which will be expensive and inconvenient, to a lithium (ion) battery that recharges through a computer's USB port the minute you plug it into a computer. You should consider this.
Finally, the price and all things related. You want to get the most "bang for the buck" now that you've taken the trouble to learn all these things. Examples of all things related would be shipping charges vs just going to a store and buying it or getting free shipping; also what it comes with, i.e. headphones.
For the price you mentioned, you can get a WORLD of features! The sum of money you mentioned is way more than you need to get REALLY NICE players! By the way, the IPod is a little like the Mercedes; you pay for the name. There! I almost made it without even mentioning any brand names or engaging in the war.
One more note: There are lots of utilities that will convert songs on CD's to MP3 format, including Windows Media Player, so, for me, all these music service thingies (like ITunes) aren't even a consideration in determining which player to get.