to be honest your best bet would be to download a copy of MySQL
http://www.mysql.com and use that with a DLL such as MrTAToads SQL DLL, I haven't used it but I heard people talk about it.
Access is ok for some situations but I wouldn't recommend Access as an online database as that's not what it's used for whereas MySQL is used for that purpose. MySQL is fast, accepts just over 100 simultaneous connections, which is a split second or less lol where MySQL is concerned.
so, MySQL with online games could make an awesome combination, but it's just a matter of setting up a Data Source Name(DSN) so your user can connect to the database at real-time.
also, you could just write a simple flat file database using C/C++, as C's file handling is extremely quick and would suit your needs instead of using Access or MySQL.
Do not anticipate the outcome of the engagement, let nature take it's course, and your tools will strike at the right moment - from "Tao of Jeet Kune Do" by Bruce Lee