Can ATC provide VFR flight following to a VFR aircraft in class E airspace?
They can. I often pick it up here in the Northeast since the airspace is fairly busy. Generally speaking I was taught that flight following is always a good idea. It is a useful tool to you in the cockpit and can provide advisories of fast moving hard to see aircraft as well as those that may be approaching to overtake you. Generally it helps to improve your radio skills and may reduce your work load ultimately.

As for who to contact, that can change. I had this very question during my training (asked here) and you can find the answer here. If you are departing from a controlled field you can sometimes ask the tower to set it up which they may or may not do. The Airport Facility Directory will have an "approach" and/or "departure" frequency listed for most fields which is generally who you call. If you are in the wrong area they generally send you over to the right controller.