I would look in the second hand market to see if you can get something complete and with parts. Check your local track out as many times there are people selling off bikes.
For something a bit different but pretty cool check out the Specialized Allez track version. I have seen these on sale recently.
You can build up the track bike but it starts adding up when you need rear sprockets and front chain rings. If you can get these with a bike second hand it makes it easier.
Cervelo T4 and Fuji Elite are pretty nice too but would stretch your budget out a bit much. You do not need to be riding on the best wheelsets which keeps your costs down… unless you want disc wheels.