Dolan sell through ebay, I got a Precursa from them for £399+£20 posted which is the best deal I could find for a decent starter. Mine came with a road fork: drilled for a brake and slightly more raked/offset but just a tad.
My club has Fuji tracks as the main loan bike, they’re ok but heavy. There’s an aluminium version these days too.
Wheels need to be bolt up, rear 120mm spaced (same as road IIRC). Cranks tend to be internal BB to keep the q-factor low. High end track cranks now have external BBs. Chains and sprockets are either 1/8″ (traditional) or 3/32″ which is the same as road. 1/8″ chains aren’t designed for flex and as such tend to be recommended for track. If you have some road parts to build with then get 3/32 parts. 165mm cranks keep you clear of the front wheel, I think road cranks tend to be 170-175.
Also have a look at a gear inch calculator to see what ratio to go with, 81″ is a beginner’s gear with Manc recommending 84″ for their tasters.
Ebay user matttempleton’s shop’s called Single Speed Components does parts for cheap. I just got a new Dicta 15t sprocket for £5.50 posted, I’m chuffed with it!
Drop bar sizing appears to be narrower than road too, with the pros using as narrow as 33cm for aerodynamics. Don’t go too narrow to start, it’ll just be uncomfortable!
What parts have you got? Have you got a plan for the build?