Hell, I'm no genius or expert.......
but it really does depend on several key factors;

application / usage
---- light load / heavy load
---- entering data / altering data/ processing data
connections / users
---- light / moderate / heavy
---- short periods / long periods
time frame
--- needs to be built yesterday / a couple of days / ages to go

I think these are the three main keys to making your decision!
If you only need a light horse to run quick and simple courses with only a few riders, then go with Access... it's simple enough to use, does the general things in life quite well, and generates a front end with the greatest of ease.
If you want something that can shift earth whilst running, entertain a large audience and don't have to beat a clock, then go wiuth myssql, (or just about anything else!).

Oh, and to chip in on the anti-access..... I've never, ever had a problem! I think it has something to do with they way they are built! I've "seen" MSADB's that fall over every tuesday at 09:00 every week for a ever, then I've used others that have crashed only due to stupidity! If it's used for the general tasks it was made for ,(note:- not marketed for - MS "claimed" so much, and it fails those goals!), then it's fine.... start trying to get to clever with it, and it has a fit!
It's a good little lightweight data sorter and cruncher, and easy to use so long as you ignore the helpfiule (:giggle..... so don't bully it... just because it's not manly enough to serve 35+ simultaneous connections all altering similar records and viewing the same data tree.... I wouldn't cope either!