Nancy, I've always kept two sizes of bow saw..one with wide teeth and another with smaller teeth. Depends on what I'm sawing. Wide teeth are faster but small teeth do a neater job with less tearing of bark especially if you forget to undercut.

Do you have a certain brand that you prefer? I bought a Corona pruning saw - folding- but it seems so flimsy. Wow, really good rain today! Nancy

Felco pruning saw is my recommendation without a doubt. I've purchased a variety of cheaper saws, including the Corona brand. No comparison to the Felco.

I prefer the bow saw design to the folding design for branches and good pruning shears and lopping shears for twigs and soft plants to the medium size (1") branches.
Whatever saw you wind up with, don't forget to undercut so you don't peel off the bark.