Access 97 1 GB
Access 2K+ 2 GB
Usually, if you get to about 85-90% you will start to see performance problems but it depends on transaction load, network configuration and several other things.
The next (big) step is to Oracle or SQL Server (the mainstream products). Things like Sybase, mySQL and a few others can increase the size limitations.
Via ADO / ODBC just about everything is "compatible with VB" ... although some are easier to program. I find SQL Server not too bad while Oracle is (for me at least) more difficult. That's probably just my amateur status with Oracle talking however.