You can use Access, if you want. It's a honest and simple DB! I used MSDE and Access. Access act as a file server, so your LAN will probably have to work harder than using MSDE. MSDE acts as Client\Server, so your server will probably have to work harder than using Access. Access is weaker with transaction, but very simple to administrate. I started using Access and ADO, not ADO.Net. Now I'm converting some my programs to use ADO.Net. It's not very far if you use a connected way. Ah.... remember that ADO.Net is mainly designed to work disconnected and, anyway, it doesn't implement a pessimistic locking. In most application, it is not a big problem, but you have to face the fact that the record you are editing on your PC, could be cahnged by other users on your server located DB!
I've not an experience with MySQL, but I think you will not have problem... there are many developers that use it and many tools, I guess.
Anyway, if your is a professional application, probably the problem should be which is the best DB, not few hundreds of dollars to buy it. For example, MSDE is free and it works with SQL Server core. You can easily upgrade it to SQL Server when you exceed 2 Giga of DB or when there are often more than 5 users connected to DB at the same time. In this scenario, probably you can spend a little of money to buy a license!
Good job!