For the language choice, if you are all familiar with VB6, it would be easiest to migrate to VB
.NET as the syntax will be very familiar.
The other choices pretty much make themselves. Your client/server desktop apps will likely be done in windows forms applications, and the classic ASP apps will become ASP.NET. Of course, you could always choose to migrate client/server desktop apps to web apps if you like. It will be important to evaluate the capabilities of those applications to determine how they will work in a web environment. Obviously, it would be hard to change a graphical design application into a web app, but a data entry/management application can very easily become a web app.
Might I suggest the Wrox book ASP.NET 2.0 Instant Results.
It provides a slightly different format to the regular programming books. The book is broken down into several applications and takes you from start to finish in creating each application. This might be a good way for your team to get started with understanding ASP.NET application. There is a pretty big difference between classic ASP and ASP.NET. I came from a classic ASP background and it took several years to get into the groove of ASP.NET.
An important .NET feature that your team should understand is its OO capabilities. This is another departure from the way VB6 works.