sticking Access behind a webserver makes it client server. Whet ever you are using for webserver does the client server but and you end up with one sequential pipe in to the mdb. Not my first choice solution, but I've talked to guys who seen to know their arse from their elbow, who calin up to 50 'simulataneous'users.
Other that than that if you want a progressiom, port your access db to sqlserver(wany easier becaause they are both MS) At that pioint chnage your connection string in VB and job done (nearly sort of maybe). The thing you ahev to remeber about usinga desktop db like access verus a client server DBMS i the optimisation strategiies are inverses.
In Access it doin saya select * from Table and then locating the record is the 'best' way to go. With Sql Server or MySQL it's insane. Select f1,f2,f3 from T1 where f1 = v1
is way more efficeient.
As far as web based stuff goes, that's much more about vb vs ASP.net, or PHP or whatever than MySQl vs access.
Pick a tech make a start, ffs don't for get security e.g. sql injection though.