Best $500 System?

you can do better than a boom box

best bargain will be to look around a college campus as students leave for the summer

2nd best is to find a used stereo dealer in your town

for new, I'd look for a Marantz receiver (or Yamaha) and some small speakers along the lines of the old LS3/5a - Epos and many others make them - you will sacrifice bass to get a good smooth mid-range

Denon also makes good CD players

Next level up is brands like Oppo, Cambridge, etc.

I like the powered monitors and CD with variable output. KISS it. Active Quad 11l/12l (best as nearfield, but great all-round), Tannoy Revolution, etc.

I'm impressed with the JBL 4208 (and 4206) as an inexpensive pair of used speakers (not active) if you buy an amp. For a sweet top end, try some older Mission speakers. Heck, $100-200 can buy a lot of speaker for the money. I have a high end system, but finding the best "bang for the buck" is always a blast.

There are a pair of Epos 3s that came up today. Can be had for $180 including shipping. Pair them with a used integrated. Otherwise, a Pioneer A20 can be had new for $270.

The amplified speaker route is also viable. Get a pair that has the volume and amp in one of the speakers which drives both speakers.
Some have a built in DAC so that disc player can be run in via digital out. 

I suggest the audioengine HD3. They are amplified, veneered, and small. Perfect for a woman not concerned about bass. The JBL 305s sound great for the money, but I don't think many women would accept their looks. The Vanatoo Transparent one is my other suggestion. Superior sounding to the HD3, but $100 more in cost.