Doesn't sound like you are sure what you are doing to play the tracks. It seems you might mean a CDG player, but I think you should reconsider. They cost a lot and leave no money for mics and mixers.
The cheapest way to go is to use an existing home PC for a player. You can get KaraFun and usually both 1) play downloaded karaoke tracks from a legal site like Tricerasoft and 2) play purchased CDG disks.
Your guitar amp is not going to sound very good for vocals. Players like the Vocopro GigMan and Duet will be easy to use, but are going to sound fairly cheesy. If easy and cheesy is what you are after, get a player like that and go have fun.
If you are looking for something higher end and better sounding, go with mixer/mic/powered speakers.
If you really have a hard $300.00 limit I would use the PC for the player, then:
1) buy a single powered speaker like the Harbinger 12", $150:
http://pro-audio.musiciansfriend.com/pr ... sku=620806
2) a small used Yamaha MG82CX mixer from EBay, about $90.00
3) two Behringer XM8500 mics, $40
http://www.amazon.com/Behringer-XM8500- ... B000TTRGUE
4) 3 whirlwind XLR cables, $25.00 (two for mics, one for speaker):
http://www.zzounds.com/item--WHRMC20
5) one patch cable, $7.50 (connect mixer to speaker XLR cable):
http://www.zzounds.com/item--HOSSTXM
6) One PC to 1/4" adapter cable (you might have RCA version already, connects computer to mixer):
http://www.zzounds.com/item--HOSCMP15
The above will hook up something that will work. You could expand to a second speaker later.
Or possibly for $130 more:
http://pro-audio.musiciansfriend.com/pr ... sku=631033
If you think you might want to do this long term, consider spending more on the speakers and mics. Better ones will make a big difference.