Timbo's Catalina 22 suggeston is an excellent one, it's the classic trailer-sailor & a perfect daysailor for 4-5; a bit small for weekending with 4 but fine if the kids are small (has a v-berth in the bow big enough for two adults to sleep in, and two quarterberths on the aft sides of the cabin suitable mainly for kids). There are other comparable fiberglass models to keep an eye out for (local craigslist is good source, also Sailboat Listings - sailboats for sale and Sailboats for sale from Sailing Texas, buy or sell your sailboat, free sailboat ads.)... I have a Santana 21, very similar to C22. MacGregor/Venture boats are decent trailer-sailors excluding the 26M, my in-laws have a MacGregor 25, a bit roomier in cabin and cockpit than C22. San Juan 21/24 is another option. All of above available $<5k in excellent condition, as cheap as <$1k needing some work. There are various similar but less popular types, look for swing keel or retractable centerboard if you're planning to keep it on a trailer in the backyard. If you have access to affordable dockage or mooring & want to keep it in the water, your options go up a bit. Catalina 25 is a good family boat.

You don't need to know how to sail before buying a boat, but it may well save you some money and grief. Basic sailing courses (ASA101 or equivalent) tend to be fairly cheap, you can knock it out in a couple weekends for $400. Rather than take any of the advanced courses, I'd hang around a yacht club on beer-can-racing night & ask if anyone needs extra crew (someone always does). Be honest that you're a beginner, & you'll learn a ton quickly.

If you go to buy a boat, take a good looking at the standing rigging that holds up the mast. It's expensive to replace and beat up on many trailer sailors because the mast is set up and taken down often. Looking to make sure turnbuckles aren't bent or cracked, the chainplates they connect to are well bedded in the deck & not bent, the stays (wires that hold up mast) don't have any strands coming out...run your hand along them & if you get pricked by loose strands, the stay needs replaced. Take sails out of bags & make sure not ripped or rotten. Old sails are inefficient but fine if you don't race. Ask owner to demonstrate putting mast & rigging up, see how he routes the sail controls; with a family, you don't want an arrangement that really clogs up the cockpit, which can already be small. If it has a swing keel take a *very* good look at the retract cable mechanism, they wear out over time and one breaking is a huge hassle at best and can sink the boat at worst (ask me how I know!).

I'm not hugely familiar with wooden sailboats but most I've seen tend to be quite old, and generally come in two flavors: beautifully restored (& expensive), and complete wrecks. I think there are more that have been kept up in the northeast.