I went for a Cinelli Parallax in the end, went around the houses on this as there seems to be no consensus on what makes a good track bike and you could spend £1400 on one. I had a really good deal on a second hand one (which turned out to be as new) saving about £300 on the price.
From what I gather you can't have any unnecessary sticky-out bits on the bike, so no brakes, bull horn bars, have been told that you can't have any Garmin bits on the bike for Accreditation (most people have Garmins on the sessions I go to), no braze-ons although you can cover them up with foam if you have them. 165mm cranks max and BB height no larger than 11inch, reason being the cranks will gouge the track if they are any longer. I couldn't find the BB measurement on any websites but apparently all the main manufacturers track bikes are to this spec, Specialised langster being the only anomaly. No SPD's Look pedals are OK. Have never seen anyone riding a fixie so I guess converted bikes are frowned on! I have got a stack of spacers on my steerer at the moment and that was OK. Tyres need to be slicks conti supersonics recommended, or Vittoria Diamante Pro Pista. Michelin are banned, tyres need to be sanded and rubbed down with meths. Asked about tyre pressure 120psi depending on how fat you are! If you have new tyres you have to ride them in gradually. Phew!!
Sounds like a lot but if you have a built for purpose track bike most of that is covered, what I discovered with mine was that the gearing was too low for the track, and the tyres were for more suited for road use. Mine came with 48/17 but I changed the sprocket to a 15 which (I think) is the same as the hire bikes, which is still quite low but probably safer to try everything out on, less likely to slide the back wheel I guess!
I have seen some TT bikes going around the track on a private booking, testing out some (extremely) expensive looking wheels. So you can take a road bike on there although you are limited to how high up the bank you can go.
Be good to go to the track with you once you're better (no excuses with that many bikes!), been looking for some OVW company.