1. a pair of BMB speakers - about $500 (other choices include vocopro, RSQ, and other PA speakers) - they are a lot cheaper in China, only RMB$1,000 a pair
2. BMB or vocopro mixer integrated with amplifier $600 (you can buy amplifier and mixer separately, but it will cost more)
3. Shure microphone (about $100 each)
4. VOD (you can ask friend to bring them back from China, a lot cheaper) basically they are simplified computer with large hard drive and software to play songs
5. Some speaker and audio equipment wires (about $50 to $100)
If you don't want to do above, at least you will need mixer, microphone to connect to your home theatre system
The lowest cost solution will be buying a karaoke dvd which nornally comes with mirophones, basic mixer function and a lot of songs though you won't sing most of the songs provided.