Howdy!
We have a few British people here, but most of the equipment postings will be from a U.S. perspective.
Much depends on the size of your venue. You can make a lot of PA systems work for you. For a small pub, the usual assumed venue here, there are a lot of choices.
On the low end, people will recommend a powered mixer from Yamaha or Behringer along with 15" speakers from Peavey, Yamaha, or Behringer. Microphone recommendation will be the wired Shure SM58 for karaoke (indestructible, tolerant cardiod pattern, decent sound). If you insist on wireless mics some people claim cheap is OK -- I prefer the AKG WMS-40 as a compromise between ultra-cheap and the $600 microphone.
A subwoofer makes a big difference. I think if I were a mobile DJ, I would be looking at the B52 Matrix units.
Then you have music, which is a whole different subject on its own. You can buy the Supercore package before you spend 10 more minutes, because everyone will recommend that as a starter. After that, SoundChoice Foundation is the best quality starter package. The UK has an excellent label in Zoom, and a good one in Sunfly.
I think we need an FAQ here.
Much depends on the money you want to spend, and how portable you need the setup to be. Here is a good thread that discusses the choice between powered mixer, powered speakers, and separate amp:
http://www.karaoke-forum.com/viewtopic.php?t=13312
Enjoy your time here! It is a great place -- loosely moderated so there is a bit of friskiness, but outright flaming is not tolerated.
