You are going the wrong direction using you stereo for your karoake. Possibility heightens you could blow your speakers because they aren't designed for live vocals & you probably don't really want to take that chance. Would recommend getting a small PA or all in one karaoke machine that you can dedicate for singing. Although in may run a little higher than your planned budget of $300.
The TV display can still be used.
For home use, this will probably fit the bill for you.
http://www.karaokewh.com/item_details.c ... raoke.html
Also right now gives you 2 30 song packs of your choice (from the list) & a 5 song custom disc plus half off shipping.