Excuse me while the old former BMXer shares the little info that he remembers from back in the day...
Two of the most important aspects of a good BMX bike are weight and gearing.
If your bike is too heavy then racing it will be like lugging cement around the track. Your goal is to get components made of aluminum and chomemoly and, funds permitting, carbon fiber.
Hardened steel or heat treated steel is a bad thing. It's uber-heavy and it's inherent ability to not bend but break could spell major injury for you if you're in the heat of a jump and your landing causes your bike to disassemble itself.
The importance of gearing I can not stress enough. Wrong gearing can leave you exerting too much energy in trying to get the bike to move or can make you spin your legs like a hamster on a wheel and move you nowhere. The key is to find a gearing that, according to your weight, your bike's weight, your physical abilities and even the track, will move you out of the gate fast and yet give you the power you'll need for any uphills and especially the ending.
If my memory still works, I used to run a 44 front ring and a 16 rear gear. I used my legs and forward momentum to get me out of the gate fast (within the top 3 riders out consistently) and I had the gearing to get ahead and stay there. Being super skinny but tall back when I was racing, I probably had a slight weight advantage over my opponents and that seemed to work well with the 16 rear gear.
I remember swapping out rears, from 14 to 15 and then 16 teeth, and the 14 and 15 made me spin too much. You'd be surprised just how much difference 1 tooth can make so be prepared to experiment to find what works best for you.
The names and manufacturers have changed a lot since the early to mid '80s when I ran but one consistent has not changed...much...and that's the fact that if you want to run a good bike, you will not find it at a department store or a big box store. You'll find it at a bike shop or through buying used. Avoid Huffy and Pacific. Avoid most Mongoose bikes (they're not the company that they used to be) and Schwinn (ditto).
As far as what to buy...I'm clueless these days. If we were talking mountain bikes then I'd have a ton of recommendation but best thing is to check out local independent bike shops to see what's currently available.
fyi: I used to run a GT Pro Performer long frame, Redline fork, GT laid-back seat post, GT Pro Performer bars, ACS Mike Buff Z-rims, DK neck, Shimano modified brakes and other stuff that I hand-picked specifically for racing and mild street freestyle.
I do wish that I still had the bike but my mom sold it (with my permission) when I moved to Cali.
Sad thing is...she sold it for $80.

Whichever kid that got it, got a close to $1000 bike for under 1/10th the price.
I know that it's extra cold here in the northeast U.S. so getting track time is going to be rare but it's advised that you ride as much as possible, both on-track and off. The number one physical thing you'll need to race is stamina...the ability to get around 1/4 mile as fast as possible without dying before the end. If you have a local track that allows off-time access then take advantage of that every nice day that you can. Learn the track, learn how to get over obstacles without getting too much air (the more time you're in the air, the less time you spend pedaling and moving forward), learn how to take turns properly (usually enter low, shoot high and then shoot low again but every turn is a bit different), and learn how to get out of the gate quickly.
Hmmm...I remembered more than I thought.