Good advice so far so let me add in a few disjointed thoughts perhaps not yet mentioned.
1) Re: size - Make sure the boat will hold the # of people you expect to be on it. 2 + 2 kids is easy but if you're bringing along friends and their kids ... Think more about weight capacity than # of seats. You may also want to think about how much time out and about on the water you'll typically be spending. Long times might indicate a need for a head (even just a porta-potty) and these are better on the larger bowriders.
2) Re : engine - Stay with a V8, 5.7L min. I'd prefer fuel injection for guaranteed, easy starts but others will tell you the a properly maintained carb setup works just fine. As far as Merc vs VolvoPenta .... I'd recommend the VP DuoProp over the B3 simply because Merc had problems with corrosion on the B3s "back when". While I think they mitigated it, they never solved it and frankly they denied anything was ever wrong with the B3 design. In your price range go for the 2 props over any single prop drive.
3) Bowrider is a good choice, indeed the most popular choice for all the reasons mentioned. Again if you think you'll require a head onboard, actually try out the compartment for size. Some are OK, others way to small except for kids. Also with BR's I'd like a door or windblocker to be available to seal off the bow from the main cockpit. This is pretty rare and while not a must have, it's nice on those colder days.
4) Will you be getting a trailer ? What do you have for a tow vehicle ? How big is your slip ? What draft will it support ? Again this goes back to the size question.
5) I'd recommend you get some form of bimini top, either when you buy the boat or budget it to add it later. You'll want protection from the sun. Make sure you also get some covers for the cockpit and bow. All preferably from Sunbrella (or like) fabric.
6) Condition over hours but within reason. I think the average hrs/season is about 40. Frankly given your budget, there are all sorts of very nice boats to be had.
7) Re: make - Certainly Cobalts and Formulas (Formulae
) are nice, I know a lot of people who've been very happy with their FourWinns and Rinkers. Find what you like vs what someone regards as best. This is Winnipesaukee, not the ocean. You can visit all the marina's in a days drive so ... visit them all. Most also have online listings. If you're looking off the lake then I'd be sure it was a fresh water boat. I'd avoid anything left in the ocean. For your 1'st used boat I'd go through a marina rather than a private sale.
8) If possible test drive with all or most of your family onboard. Then you'll see if the time-to-plane and ride are acceptable to all. Also be sure the gears (Fwd-N-Rvs) shift smoothly and predictably.
9) If you're going to spend time hanging out, anchored at the sandbar, it's best to have someplace dedicated (at the bow) to store the anchor and rode. Also you can't have to many cleats. Look for them amidships as well as fore and aft.
10) Check out the (re-)boarding ladder. If you're going to have people in the water then they'll want to come out and back onboard at some point.
11) Don't get a boat w/o snap-in carpeting. Glued down is bad. No carpet is hot (but can be fixed ... with snap-in carpeting).