I've always been impressed with Postgres; it's traditionally had a more complete feature set (in terms of ACID compliance, support for advanced queries, etc.) than MySQL, it has solid Windows ODBC drivers, and its documentation scrupulously points out any areas in which it deviates from the SQL standard. (All databases, it seems, deviate in one respect or another, but Postgres is the only one I've seen that makes sure you know when you're doing so.) I haven't tried the usage scenario you describe, but I've had no problems running it on Linux and accessing it from both Windows ODBC and Linux clients.
I don't have any experience with Firebird; sorry.
