Building a track bike

I’m thinking of building my own track bike, for riding on tracks, not a fixie for the road. Apart from the frame, I have pretty much everything I need already in the shed but I have a couple of questions about the build that some of you regular track riders might know;

1. Any suggestions for suitable clincher tyres for the track?
   
2. Handlebar width - on the road, I ride 42cm bars - for the track, should I stick with this or go narrower/wider?
   Thanks