The border can be anything that will compliment the squares. If you are going to frame them, you may be able to put a stabilizer behind them (like in a t-shirt quilt). If you have a good framer in town you might ask them for advice. I had one they stretched it onto a backboard and used the mat to frame it rather than fabric. But a friend of mine did it herself, put a fabric border and stretched that one the board and framed it. You have several options.

there is a light weight fusible used in clothing that would be good on the back of your blocks. would make them not so thin and stabilize them more. comes on a roll, just ask at Joann's. it's permanent, doesnt' wash out.
also you might have room to add some colorful corner triantles to the blocks. have fun.

Lovely work. Once you've decided what you want to do with Grandma's embroidery make a sample or two. Get comfortable with your skills and then work on them.

If you want a country look, you could frame them in an old window frame that had 4 panes. Sash if necessary w 30's repro fabric, color to match your decor. You may wish to have glass put back in the frames to preserve the fabric.

I realized my miss-type. Want to make it for my mother, she was her Mom

ditto. 30s prints or feedsacks and borders

So sweet! I inherited some of these and I am planning to frame them in 30's prints (probably log cabin) and make pillows.

I agree with the 30's prints .........and I also HIGHLY suggest the stabelizer. The fabric she probably embroidered them on are called "tea towels" and the fabric is VERY flimsey and ravels easily when cut. So look for a stabelizer that will be flexible and soft when quilted --- so you don't have a stiff area on each block. I'd also stabelize the whole block....not just behind the embroidering. Will be ADORABLE!

awesome idea there!

Thanks for all the suggestions