Elizabeth, also think that what's being published now was acquired a couple of years ago. But yes, do spend some time browsing the PBs in bookstores and libraries and note the ones that you like particularly, or that fit your style of writing. You can then approach these selected publishers with your work.
I laughed about constraints because I write for the educational market and sometimes there are 50 different specifications that need to be met. Believe me, it's like putting a puzzle together, trying to write a story with limited words. But it's also very enjoyable. For instance, for a book about textures, I wrote all about cats -- their soft fur, the rough tongue, the shiny ball, etc. Turns out, it's one of my favorite books :catlove
Happy writing, Vijaya