No, you don't want something like that. Even if it sounded better than anything you could imagine. I have seen similar record players for sale at Rite-Aid, by the way. You want to avoid those USB ones, too, at least for day-to-day listening.
Even with powered speakers or an amp you still probably want a preamp, unless you have a receiver that has a specifically marked phonograph input. Most amps expect a signal of a certain strength. If they don't get it, you can turn them up and get a loud enough sound, but it usually will sound tinny.
So with that I currently have a $100 Sony turntable I got from Circuit City. Not that hot, but it works, and is in the range of what your mother was probably expecting to spend. You can get a belt-driven Technics for about $150 usually.
There's a sweet spot with stereo equipment after which you start entering audiophile kookoo land and diminishing returns. I say starting at around $500 you start getting really high quality, durable stuff.