i use balsa wood cut to size

That's what I would use :)

I cut up some plastic place mats, they work great.

I use a piece of cardboard box or cardboard they wrap fabric on, most stores are happy to give them to you, and wrap it with fabric, like a gift, which I glue down. Let the glue dry completely then just put it in your finished purse and it is easily removed if you want to wash your purse.

There's something similar to foam core, but more durable. It's just as light. It's called Rag Board - thicker and stiffer than regular mat board. Ask your local frame shop to cut you a piece to size. (Micheal's keeps it on hand; others may not.)

I have used Plastic Canvas, I did not care for it as I did not think it was sturdy enough. I now use a think plastic that the Amish use on their dress bonnets I don't know what the name of the product is, I buy if from my Amish ladies. Light weight, comes in black or white, and is flexitble with the bag.

I've use plastic cross-stitch canvas. Over the years I tried other things but always went back to plastic canvas. Overall I like the firmness of this product. If I have a cutting mat that is no longer usable, I will cut that up and use as well.

One of the best totes I made had a bottom made from a piece of adhesive vinyl floor title. I covered it in left over batting and made a sleeve out of lining fabric. It doesn't crack...isn't heavy...and holds the purse shape. any of the hardware stores have this. We had some left over from a home project

Plastic Canvas

I've always used plastic canvas. Works great: bendable, but rigid when it's in place. I like it best for the fact that it is light weight! You'll like it.