There are online "web stores" packages that can handle stuff like that easily.
but think twice before you get into this. The moment you offer on-line registration, you have the hassle of how to take money. People will want to use PayPal. Do you want to deal with that?
Many people will balk at sending their VISA or MC or AMEX numbers over the web, to pay. Those that are OK with it will still be aware that it's been done. Do you want to be the first place those people come looking when they have an identity theft issue, and $5,000 worth of unknown charges appear on their bill?
It's a doable thing, but there are issues.
Having a Web form that people fill in to register for races is brain-dead easy. It's the money transfer that's the nightmare.
1968 Selmer Series 9 B-flat and A clarinets
1962 Buesher "Aristocrat" tenor saxophone
Piper One Design 24, Hull #35; "Alpha"