I have not run into any multi-user conflicts with Access, but admittedly the three Access-backend apps I developed were for small numbers of users. There's no simple answer: the back-end you use will depend on the scope and type of the project. Havign said that, here are my own preferences these days for use as a backend if, indeed, you have decided to code the front and middle layers in VB:

-- SQL Server. Pros: Security, power, well-known database, great integration with ADO. Cons: Expensive, might be overkill for your project.
-- Access. Pros: Security, price, great integration with ADO, sophisticated users can take advantage of Access reports rather than relying on your app's own canned reports. Cons: not as powerful as SQL Server or FoxPro, some multi-user limits after a few dozen users.
-- FoxPro. Pros: Power, price. Cons: No security; at least at the moment, not great integration with ADO; some client resistance to using an unorthodox backend

It really depends on what you are going to do, for whom, and what your current skillset looks like. This drives some of my FoxPro friends crazy, but I have to tell ya, I would hesitate recommending use of VFP as a backend to someone who doesn't already have VFP skills - I am not sure it's worth learning at this point -- it does provide a backend with tremendous power without the cost of SQL Server, but so far, I have found that clients who need the power don't hesitate much on making the investment.

I had a conversation two days ago with a guy who does a lot of VB front/middle and Oracle backend, and he rather likes Oracle. I can't really speak much about Oracle, though.