Check Craigs List for old Catalina 22's.
catalina22.org
They can be found for pretty cheap (less than $2,000) and are a good family weekender lake type boat. Most of them have a swing keel so you can retract it, put the boat on a trailer and take it home, vs. spending money for a slip.
A 19' Flying Scot
FLYING SCOT SAILBOATS - The Best Daysailer in the World is a great lake boat and a 17' Oday Daysailor is good too, but no cabin if you want to sleep on it.
http://boats.smartcarguide.com/o-day-17-sailboat
Probably the best deal if you're new to sailing is to go to a nearby sailing club, see what they've got for club boats. Usually once you join the club, you can use their boats anytime they are available, and for us Airline types that works out, because the 9-5 M-F guys are only at the clubs on the weekends, while we are flying, so you'll have the pick of the boats on your days off during the week.
Most yacht clubs have a kids program too, and adult learn to sail programs, on the weekends, so you can drop the little darlings off there, they'll jump in an Opti,
Optimist (dinghy) - Wikipedia, the free encyclopedia
while you and mom go out on a bigger club boat.
Memebership - FAQ - Lake Lanier Saling Club
I started in little dinghys and then raced monohulls for years, but when I got my first taste of real speed, out on the trapeeze wire of a friend's Hobie 20 I was blown away;
Hobie 20 sailing from Tampa Florida - YouTube
So I got hooked on catamarans. BUT...because you are going three times faster than a monohull, spray is flying, so you will get wet if there's any wind at all. That's why my wife won't go near my catamaran. They are better in the south where the water is warmer.
Up in Portsmouth, NH we had to wear wet suits, even in July, when racing out in the Atlantic. That ocean water never gets above 50 degrees!
If you can't find a club near you, check out the US Sailing site, they have lists of clubs:
Getting started