Back when Norm Sims and I built a bunch of strippers we routinely used 3/16" thick strips for most canoes without any problems. I doubt the weight savings amounts to much compared to 1/4" strips, but it can certainly be done and works fine. I know of a kayak builder or two that use 1/8" thick strips, but I'd be leery of trying something as wide as a canoe with them (plus it's a pretty tricky stripping job trying to keep them aligned with no margin for error).
Yes, the strength comes mainly from the fiberglass layers, but the stiffness and shape-holding ability of the hull comes from spreading the inner and outer glass laminations apart (the job of the wooden core between them). A thicker sandwich is stiffer. Since strip construction is somewhat limited in its ability to flex without damage, you generally want to keep them fairly stiff.
The best advice anyone can possibly give you on your first build is to find a good set of directions and follow them to the letter (strip dimensions, cloth weights, etc.). All too often, the reason that first-time builders manage to royally screw up perfectly good boats is because they get too clever and think they have a better idea of how to do something, but no experience to back it up. There will be plenty of opportunities to explore other options on future builds, but first, show yourself and everybody else that you can build a good, sound boat (spoken by a guy who has sawed-up a partially completed experimental boat or two in his day and tossed it in the dumpster...just ask Norm).