Hi Marty. Yes as the other said - listen and learn and don't be afraid to ask. A good all-round gear is 48/16 (81") but this depends on you and the track. It's a great training gear and even a good racing gear for the short, steep track that I ride on. All the rentals are 81" and it's the required gear for bunched racing. Heck the fast guys can go 36mph on that gear so it's certainly good enough for me.
Forget about the fancy bike stuff as it doesn't make you much faster - not in relationships to the dollars spent anyway. Your training & skill level will count for much more than carbon bike parts.
When our new track opened, all the old track bikes started coming out of the woodwork and it's interesting to see what was tucked away. I scored a nice classic early '70s Colnago with loads of history behind it (a few 6-days etc) and with a bit of updating it's now a classy ride once again.
Read the rules of our velodrome as there is a wealth of info here -
http://www.forestcityvelodrome.ca/index.html
Your track should have some written rules too.