I am sort of in the same boat as you, except I'm a season into the whole experience. I was essentially brand new to track racing in August 2008, then raced May-Aug 2009, maybe 10-12 times. I had two prior track days in the early 90s, kind of a "into the deep end" bit. Those were the only two days I'd ridden a fixed gear bike outside prior to my race in Aug 2008.
This is what I've found.
The Omnium cranks are fine. It appears, looking at my bike, that that's what I bought (I just ordered the cheapest track cranks out there - they cost the same as a chainring, so I just got a crankset instead of a 48T).
I'd get multiple chainrings - find out what people there use and go up and down a tooth. Racers at the "local" (it's 3 hours away) track generally use an 88-90" gear (49 or 50 x 15). I use a 50x15, and I'll be trying a 49 and 51. The 48T that came with the cranks - I couldn't spin fast enough to stay with the group.
If you're lucky and can afford a second rear wheel, get one with a bigger cog. In my example above, I'd get a 16 or 17T. This is so you can warm up. Or, if you have room, you can ride your bike on rollers. A flipflop wheel works.
For wheels, being able to spin up is good. Top speed is less relevant (at least where I race). I can't go nearly as fast on the track bike as on the road bike - in fact, my top speed on the track bike is what I'd consider to be a relatively slow leadout on the road bike. Therefore it makes sense that I emphasize acceleration over top speed.
I use a front aero wheel, mainly because my problem is in finishing races. An aero wheel ought to save me some energy, at least that's what I figure. You can use most road wheels if you have a "track skewer" which has no lever; instead it has something like a hex head on each side. Next year I'll use one of my road front wheels for track racing. I'll focus on getting track rear wheels since I only have one, and it's a light rim built heavy (2.0 straight gauge spokes). I want to rebuild it with an aero rim (Zipp 440), and then hopefully get a second wheel (or, preferably, a second complete bike).
Nothing wrong with quill stems. They're quick to remove, they don't require headset adjustments, and you can easily carry a few around. Problem is swapping bars etc. I have a few quills and I figure I'll set one bar up for time trials (pursuits, maybe kilo). I'll use the setup I have now otherwise (crit bend road bar).
My bike, kinda sorta (it changes):