I have SS school and while it seems good when up and foiling I struggle at times starting due to the weight of the foil causing it to instantly sink. Light onshore I end up in shallow water and hit the bottom.
Would a lighter foil such as the Zeeko be easier plus in general is a lighter foil just better?

I think so. A light foil thin board combo works real well for water starts.
My home build floats on its side as the foil its self is buoyant.

Lighter is better if its is as strong and stiff. Carbon is the best option if you are keen to do the sport for a long time.
The weight of the board is important to, like Plummet says a board you can easily start on makes it easy.
The reduced weight really helps when getting up and going and with control when you are going.