If you are using ASP already, I suggest you to continue, simply upgrate to MySQL or MSSQL, with MySQL you need the ODBC connector available at www.mysql.com if you don't feel like using ODBC, you'll find some free drivers out there for direct communication with MySQL, MySQL is very good, and if you are using Access databases I don't think you have 1000's of gigs of data WHICH MYSQL SUPPORTS, for data integrety try InnoDB type tables which are fault tolerant, but the server needs to have enough memory. Otherwise use the default MyISAM type tables also good and not memory hungry.
I've been using ASP/MySQL for quite some time and couldn't be happier, the next major release of MySQL (5.0) will support stored procedures.
It's so easy to use and manage MySQL, that after you use it, you would be asking yourself why have you not done so before.
Better than that would be ASP.NET and MSSQL.
I don't use PHP because I do well with ASP/ASP.NET and only manage Windows servers, PHP is not better than ASP/ASP.NET it's just more focused to L/Unix servers.