You cannot run your Access application directly from a web-based environment, at least not in this version of Access. 2010 has some web-enabled capabilities, however, and may be suitable for your needs, but I'm not sure when it will be released.
That said, the traditional path for this would be to either (a) convert to a web-based language like ASP.NET or (b) setup a Terminal Server for your remote users. If you have a LOT of users, and don't know who will be using this, then (a) is by far the better approach. Terminal Servers require licensing, which can get fairly expensive, and require a good bit of care and feeding at times. Web-based frontends are often easier to deal with, once they're up and running.
Also, as you mention, SSE is a much better choice for web-based stuff than is Access IF you think you're going to have more than about a dozen users. If you're moving to ASP.NET, then the move to SSE or full SQL Server is a no-brainer, since the .NET environment is very tightly coupled with SQL Server.