Sorry for the lengthy question, but here goes:
I currently have an access database with a FE and BE that resides on each users laptop. Weekly they connect to the network and synch the BE the master on a network drive. There are numerous propblems with this as it has grown quite extensive.

We would like to have this be a server based database with the remote users either having access through the web or something else?

A few of the capabilities of the current database:
1. generate and print reports 2. update project forms. 3. enter time logs 4. enter notes

My question is:
What are my options for a remote FE? I am well versed in VB6 and Access. Would be willing to learn other languages (, my SQL, etc.) Would I be able to have the same functionality or would I have to have separate software for certain functions?

I'm not sure what you mean by 'FE' or 'BE', but if you are planning on mounting this database on a web server I suggest you forget about using Access. Actually Access is not even the database, but Microsoft's front-end to their JET database.

It is not designed for multi-user use.

Look at MySQL or some other RDBMS. Anything you can do with your current set up can be done in MySQL. It's a matter of migrating your data over, and writing the program front-end.