The popular karaoke mixer brands are Acesonic, Behringer and VocoPro. There are many more brands but these are well established brands with a good reputation for sound quality and durability.
If you are connecting a karaoke player to the mixer then it will have a stereo connection which is already two channels on the mixer (one for the left sound and one for the right sound). The microphone will take one channel per microphone.
Most mixers are compatible with existing stereo amplifies and it is usually as easy as getting the correct cable to connect them properly. I suggest you take a photo or make a note of the sound input connections on your amplifier and make sure you can get the correct cable to connect the mixer sound output to your stereo before you buy the mixer.