Sounds like you are on the right track. As with all racing, function trumps form. And generally speaking, form costs extra.
You will probably fiddle with your fitting for a while since this is new to you. A threaded to threadless adapter will make fitting a bit easier and give you a lot more stem options. Plus, if you find that you need a 90mm stem instead of a 100mm, you can go to your local bike shop and get one for cheap instead of the harder to find quill stems. Threadless stems are flip/flop giving you more fitting options. Once you get your geometry settled, then maybe buy the quill stem that makes the right dimensions for the bike for you, and buy it once.
Mountain bike pedals (Time ATAC, Eggbeaters, Candy, SPD) are generally frowned upon at many tracks because they are relatively easy to disengage from. Popular options are SPD-SL, Speedplay, and Look.
You don't *need* track bars. The majority of the bars that you will see on the track are road bars. Just make sure they are strong, at least made of heat treated aluminum to take the stress of standing starts.
Most people run crank arms up to 170mm. 175s are uncommon on the track. It really depends on the steepness of the track and the pedals you choose. A flat track can easily be ridden with 175s.
Tubulars aren't a requirement. More of a luxury being that one doesn't have to worry about debris to puncture the tire and the high PSIs that you can get. But, 120PSI of clinchers is fine. Do, however spend the extra bucks on a quality tire.
A lot of questions (crank length, pedals, tires) can be answered by the regulars at the track.