I don't necessarily agree with the idea of staying away from an old boat. However, some excellent points have been made. I bought my first boat 2 years ago and it was an '81 Grady Bimini 220 with a '93 Evinrude 200 with a 2003 trailer. I had a limited budget (less than ($10k for boat, repairs, electronics, etc.).
I found this boat and had a successful survey of both hull and motor. In fact, it was local, so I went to speak with the mechanic who worked on the boat in the past. Did I need to throw some money into it... absolutely. I had to have the carbs rebuilt and install a fuel/water separator plus some other minor things. Since the mechanic was working on it, I had him change the water pump and go over the engine. It was and is running great.
The hull was structurally sound and needed a good cleaning, which I did. I did need to do some work on the transom, but it wasn't that big of a deal. I also did some minor repairs like replacing the thru hull fittings and tubing as well as the bilge pumps.
I fished this boat for the past 2 seasons and had a great time. More important, I have 100% trust in the boat ( I also have boat usa towing so that I don't get jinxed, but never needed it).
My point is that a well taken care of old boat may get someone into boating without too much financial risk. If I decide to sell this boat, it has already depreciated almost as much as it can. In fact, it is better today than when I bought it, so I should get all or most of my money back - even in todays market.
Of course, if the boat looks neglected, it probably was. If it has noticeable problems, like a tired engine. I would run away and look elsewhere.
There is some good advice here, but I wanted to give a different perspective. Maybe I was just lucky, but an old boat doesn't scare me one bit. In fact I'm looking at a "new boat" now. It is only 15 years old...
If I decide to take the plunge, you may even see my "gently used" 28 year old grady for sale...
David