Go and visit the shops on a Sat, that should be their busiest day and you will get a good idea of how the shop truly is. Is it nice smelling when you walk in, how clean is it, how friendly do the people seem to be, is the grooming area visible or is it behind closed doors? Narrow your list down from there and then go back on a less busy day and ask to see the bathing area. Who does the bathing, can you wait while they groom, do they have pictures available/visible of dogs they've groomed? What are their policies concerning injury or illness during grooming?
It is always a great idea to have a picture with you of a cut you like so that there is little chance of a misunderstanding. To say you want a puppy cut can mean a different thing to everyone you ask. Write down and attach with the picture as specifically as you can what you want. How long do you want the coat to be. Do you want the ears tipped, do you want the hairs from inside the ears plucked or just cut. What do you want done with the topknot, the hair on the bridge of the nose, in between their eyes. Do they trim the hair from between the pads, around the bum, on the tummy and inside of the hind legs. Do you want them to leave the tail long or cut it shorter. Do they cut the nails. The more info you give the better the chance of getting the cut you want.
I've got an amazing groomer, she has a great memory of her clients and what they like, but I always go over what I want from nose to tail before I hand one of the kids over. I don't want there to be any chance of an error. It's only hair and will grow back, but I'd just as soon avoid that problem if I can.
And always,
always listen to your gut. If it's telling you something don't hesitate to ask/intervene. If I thought something was wrong, even if it was in the middle of the cut, I'd ask to see my dog or stop the grooming, pay and leave. You are your babies only advocate you must do what you feel is in their best interest. I've left places before, vets, groomers, trainers, etc and I will again if I feel that something is wrong.