JET
In my experience when Jet loses network even for an instant it loses connection to the MDB file. At best the user gets a 'DISK OR NETWORK' error. at worst you get a corrupted MDB file.
I've read of success stories with up to 50 users on Jet, but I'm sceptical. Have a look at groups.google.com if you want to find them.
Remember that if you have a large number of rows in your database (it may have in the future) then your system is going to get slow. If you perform a query on Jet that retrieves 10 rows from 10,000, then all 10,000 rows are read by the client, so they have to travel across the network, whereas obviously MSDE or MS SQL Server will only kick back the 10 rows.
MSDE
MSDE apparently starts slowing down when asked to perform more than 5 concurrent batch processes. It sounds like it might be suited to your application
http://www.granite.ab.ca/accsmstr.htm has info.
We use MSDE at work, but only for a 10 user system. Not sure if you'd need SQL Server instead. MySQL is likely to be a steeper learning: the ODBC drivers were flakey when I tried them, but that was a couple of years ago.
MSDE might be quite hard work since you don't get the Enterprise Manager (GUI) for administration: we have it as a result of have one of the developer tools. You'll have to use the command-line I think.
My personal preference: ditch Jet, and go MSDE.
Dave