The absolute best person to learn from, on how to do puppets for daycares, is Dave Risley:

http://www.stevensmagic.com/shop/puppet-video-risley-dvd/

I agree with Tommy. Preschools don't have standard rules for performers. If you're entertaining, then their happy. I've never been a big puppet person, but if I see one, I like than I add one. For really little kids, I use the dinosaur in the shell puppet, which is always a fun warm up. I'm now having a ball with Axtell's Baby puppet, but some shows I don't use puppets at all, depends on how I feel that day. I mean, in 20 years, I can't remember a director ever asking if I brought a puppet.

I use at least one puppet at most shows, sometimes 2. I do vent with them, I need to practice vent a lot more, but I make make it really fun to watch so the kids aren't paying much attention to my minor lip movement, etc. It certainly isn't a requirement at daycares, but it's a nice brake from the magic for both you and the kids, and it adds variety to the show, and it's good for marketing to say you do it.

I learned directly from Zucchini - give them age appropriate entertainment and focus on the kids. If your show is entertaining, it will sell with or without puppets.