I am almost certain you can do everything you want with one chain. (I don't know your bike and the length of your track ends or dropouts.) Think both the gear inches you want (seau grateau's post above) and "total number of teeth". Say you want to ride a 72" gear around town, show up at the crit and re-gear to an 93" gear.
So: first, get yourself a wheel built on a double-sided track hub, fix gear cogs on both sides. (Miche and others). Now a 45-17 will give you 71.5", plenty close enough to 72". 45+17 = 62 (total number of teeth). A 48-14 (again 62 total number of teeth) will give you a 92.6" gear. So you show up, change chainrings, flip the wheel and race. Repeat to ride home. Odds are good that you can go 1 tooth either side of the perfect total number and stay in the sweet area of your track end or dropout.
I am a huge fan of double sided track hubs. I have two road fix gears running them. On one of those bikes, the dropout is so long I can run anything between 12 teeth and 23. The other is an ancient road bike with 1970s Campy dropouts. I have it set up to do roughly what I am suggesting for you, but with 3 gear inch possibilities and fast gear changes. 2 minutes at hill tops and bottoms. 3 chainrings. 2 cogs on one side of the hub (21 and 17) and the usual one on the other. Each cog lines up with its respective chainring. The three gears can be 38-21 = 49", 44-17 =70" and 46-14 = 96". (59, 60 and 61 total teeth works out nicely.) (I don't recommend doing this unless you have a machine shop at you disposal and/or engineering/CAD skills and/or most of a grand to burn, but done right it is really fun!)
I run all my fix gears with 1/8" chain. I really like the $20 Izumi chains. Not the quietest, but very hard to throw off and very forgiving of too much slack. Last a good long times. For the same reasons I like the Eur-Asian 1/8" cogs. (I also notice both of these are popular at the velodrome with racers on budgets.)
Ben