Ok I think things are getting a little off topic here.
To answer your core questions racketboy in one big hit...
My concern is that I'm not sure if I will eventually blow them out. I'm not sure how many watts or whatever they can handle -- probably about 50(?)
I don't usually turn the volume up too loud.
OK, like I (and others) said, if you are not hearing distortion, your speakers are in no danger. Distortion is the only way to blow speakers out (well, distortion or a really high peak in the current, which won't happen unless you crank your amp to the max). You will be fine using these speakers.
Do you think I should just stick with the old cheapies for a while?
Absolutely. For reasons why, see my next answer.
I'm hoping to get some nice monster cable to possibly increase the sound quality instead of using the cheap wire that came with them (and that is too short).
Using better cabling in this situation will not alter the sound quality. Not with the other equipment you are using. If you had 200 thousand dollars of audio equipment, housed in a specially designed acoustically flat room and your hearing had never been exposed to to more than, say, 65dB and you were 4 years old (ok...so I exaggerate) the you might hear some difference. There are some guys out there who claim to be able to hear the difference between that batteries used in their effect pedels for guitar...I'm guessing your not one of these
Lemme hear your opinions and suggestions -- thanks!
Stick with the old speakers, save your cash for buying some new ones. You get what you pay for...except when it comes to speaker cabling.
EDIT: Actually, tell us what model amp you are using and also what model sony system you've taken the speakers from. That'll clear up once and for all how suitable they are for the amp.