Hey Steven...welcome to SMF! There is tons of collective knowledge on the forum and great people willing to help and share their experiences. I started on a Brinkman as well and was able to produce good Q...it just takes a little more work.
A few things to keep in mind about the brinkman (my personal experience):
1. you will go through a good bit of charcoal/wood. I would go through about 20 pounds of charcoal for a 5-6 hour cook (ribs)
2. The side by the firebox will be substantially hotter than the other side. There is a lot of information on how to improve this, but the firebox side will be hotter. I bring this up because i often had to flip meat like ribs or brisket around to get a more even cook.
3. Always give yourself plenty of time. I found it much harder to "predict" when the meat was going to be done compared to my
Rec Tec due to overall temp control.
Those are a few things i learned using my brinkman. Like i said though, you can still produce great BBQ.
As for the race, pulled pork would be the first choice (time permitting) because it is a forgiving meat and is hard to mess up. Also, you can feed a good number of people with it. Im sure once you fire that baby up you are gonna make some new friends.
Second choice would be ribs. They are not as forgiving but take much less time.
Another option would be chicken as it doest take much to do a couple chickens.
If you search, you will find amazing recipes for all of the above.
Good luck with the new smoker. Most important, have fun and post some pics of your first cook!
Brian