The most important thing in having a pleasant and successful buying experience is to find a really good seller.
@zayerpaul was very helpful, to the point of going on a test flight with me after completing the purchase and getting the plane out of annual. He was great about fixing a few minor squawks and made the whole thing easy.
Most of the important things have been covered above. Don't pay too much attention to all the slowness wisecracks; the performance of the Sundowner and the B23 is comparable to a Cherokee 180 and, while they're not fast either, they don't get the derision of the Beeches. The early ones, with the smaller engines, were underpowered slugs, but the 180hp engines in the B23s and C23s are just what was needed. The planes are roomy, comfortable, and very well built. There's only a small handful of recurrent ADs, none of which are terribly onerous.
CG location is the key to getting good performance out of these planes and to making them land well. They've always been nose heavy, and if you put a couple of, uh, "robust" people in the front seats you can end up near the forward CG limit. Not only does that slow the plane down, it also can cause you to run out of elevator authority in the flare. I keep two 20lb shot bags and a 15lb maintenance kit in the cargo area and the plane lands just fine. I get close to book numbers in cruise, around 140 to 142 mph TAS (a touch over 120 knots).
The plane is less forgiving about airspeed when landing than a Cherokee. You need to fly the numbers, between 75 and 80 mph on final. Too fast and she'll balloon and float, too slow and she'll drop like a brick.
Join Beech Aero Club and get a copy of the "Mouse Hunt" checklist to learn what to watch out for when shopping. The club website also has a long-running thread called "Mouse Hunt Monday" that lists planes coming on the market every week. Many of them are known to members or owned by members, so you can get lots of information.
If you find a good one, don't hesitate to buy it. They're great planes.