The primary reference I would point you to is
http://www.paddling.net , which has buying guides as well as gear reviews from "regular" folks, plus a discussion forum.
Depending on where you live, there may be a local paddling club, or informal group, where you can meet people and learn a lot.
In the northeast, there's
http://www.stormpaddle.com , an informal NY/NJ/CT/PA/DE group that is mainly geared to (fairly serious) sea kayaing, but are really friendly and a great source of expert knowledge on kayaking. I met up with some of these guys are they are eager to help out newbies to the sport.
There are other club websites out there, and you can easly find them on google for your area. I am mainly familiar with DC-area groups.
You
could do "sea" kayking with small kids, but mainly on calm waters. Other flatwater like a lake or slow river is definitely an option. Kayak mfrs are looking more to the "family" market these days and are selling modest double kayaks with a third "jump seat" (like this:
http://www.kayaker.com/new/products/boat.asp?type=recreational&ID=103). Now that we have a kid on the way, this will be the way to go for us. It's basically a more stable, and faster, version of a canoe.
I say "modest" because you won't be able to stuff a kid into this sleek one (with little complaint)!:
http://www.kayaker.com/new/products/boat.asp?type=day_tour&ID=87), and that second boat is much faster than the one with the jump seat.
I would recommend against "floaties" (if they are what I think they are) and point you to a real personal flotation defive (PFD) for the kid. I think the Coast Guard and most states requires kids to have PFD's.
http://www.nrsweb.com/shop/product.asp?pfid=2165&deptid=956Little kids could also wear a floatsuit:
http://www.parents.org.uk/index.html?safety_swim-safe.htm&2 . Body Glove makes one, and I saw some at several US sports store websites.
Paddling with my 3 y/o niece has been really fun, especially in wildlife refuges and other interesting areas where you can't really walk to the "good parts." Remember to wear a hat and bring sun screen!