Access is not really suited to web serving IMO - it's ok for RADing a quick windows project (small stock control etc) but ask it to serve simultaneous requests and it'll fall over no matter how much hardware you throw at it.
SQLServer is better but cost quite a lot more.
MySQL is of comparable quality to SQLServer and is free (if you've been getting along with Access then SQLServer will probably have way more features than you actually need). MySQL also plays nicely with PHP as well as being multiplatform - you could shift the entire project to Linux or BSD without recoding any of the db stuff.
PgSQL is probably slightly better than MySQL (IMO) but doesn't exist on Windows and is a lot less popular (mostly due to its feeble PR machine).
In short, junk Access and switch to MySQL unless you actually need a feature in SQLServer that MySQL doesn't have.