Wife on board?
I'd like to chime in with what Winkfish suggested earlier - make sure your wife is on board.
If this is something you're going to like doing, and it sounds like it is, and you have a significant other, then it would be good to really discuss the hope and dreams you each have. How do you envision the future with a boat? Do you see yourself in club races? Or does she see the two of you on a sandy beach somewhere with a picknick lunch? Will she be the one hiking out to windward taking all the wind and spray?
Looking at the picture of the ad I see a flush deck boat and basically I'd put this in a sport category. For the same length, well, maybe a tad more, the O'Day 16 has a cuddy which provides some protection. My wife spent some time ducked behind the cuddy on our boat (Falcon 16) when it was cold (late fall, early spring, or just plain high wind-chill factor).
There will probably be some days that are forecasted to be nice but turn sour and you sure don't want your S.O. turning sour on this dream.
The Precision 15 with it's flush deck and the O'Day 16 with it's cuddy are two totally styles of boat. The O'Day would be a nice "family" type boat that could be used for short "cruises". Unfortunately, the O'Day is about a 45 year old design and there aren't many small cuddy-type boats in the newer designs.
As for price, just look at a new boat and the price and any of these older ones will look like a bargain - which they are. Sure, they come with some dings and scratches but if you bought a new one you're sure to put some of those on yourself.
Trailer: Tires take a beating from UV so if you wind up putting on new tires a suggestion would be to have some tire covers for UV protection.
Lake sailing: depending on the topography, can have fluky winds. I've only capsized once and it was on a small lake. Lost the rudder doing it, too. This was the only time I didn't have the safety tie on.
Sails: Might be "blown-out" which will cause more heeling in gusts. New and flatter sails will help with sailing ease because the boat won't feel like it's getting knocked down every time a small gust comes along.
Just a few additional thoughts.....