First of all, what server side language are you using in building up your site? ASP, PHP or maybe .NET?

Of course MySQL is better than MSSQL! Not just it is free and widely used, but they are fast!
Some people thinks MSSQL is better then MySQL, but that depends on your main usage! Other people just admire and love MySQL.

The advantage of MySQL over Access(MSSQL) is scalability, MySQL handles multiple user connections better and is far better suited to web applications.However Access is far easier to use and set up, to be quite frank I once messed about trying to set up MySQL for about 2 hours. I got nowhere, gave up and tried a few times again before I successfully installed them.

Access is a good PERSONAL database application, but is not server sofware and is not suited for simultaneous user connections...which web apps, by nature, require...

So back on topic...

If you are using ASP, then you can just check out my very own ASP-MySQL Login Tutorial in the ASP Forum here in webforumz!
If it is PHP then, you might want to visit this lovely PHP Login Script that I found really interesting!

Hope that's help you
Cheers...