You can find at least thirty models of DVD karaoke players with built in microphone mixing jacks on them.
One website I recomend is Acesonic.com - they are one of the better karaoke dvd player sellers available in the USA.
Googling "Karaoke Player" will bring up hundreds of US dealers for DVD Karaoke players.
Most will play CDG (CD+G), Video CD (VCD), and DVD with no problem, you can check all the specs online too!
DVD players with Karaoke function will play your singing and music through the TV,so they do not require an external microphone mixer or reciever, but they do come with the option to hook up external amplifiers if you want to crank it up.
Almost all have jacks for two microphones, and have level and echo control knobs to adjust your sound against the music.
The brands I have tried over the years are Acesonic, CAVS, Vocopro, Malata, RJ Tech / Iview. RSQ, Arirang, Vidtech, ProAudio, BKV, Martin Ranger, JVC, Sony, Samsung, and some older ones no longer around.
There are over thirty brands that can be found on the internet however getting service is problematic for any none US warrantied units, although you can buy them anyway if you like. My next player will be a DVD Karaoke play from Mad Boy Audio Model MFP-2000.
You can find units of most brands with HDMI,S Video, Composite Video(RCA coax), Component Video(RGB), VGA(PC), and Scart(Europeon) Video outputs,
And Audio output will usually be Stereo, 5.1, Toslink Digital(Coaxial) or SPDIF Optical Fiber
HDMI output requires only one HDMI cable to send picture and sound together to your TV set if your High Definition Widescreen has HDMI jacks (most have at least one).
Good Luck Karaoke Hunting!