Rules of thumb are okay for getting you into the ballpark, but beyond that they don't tell you much.
Here's an example. Last weekend I was over at Indian Rocks Beach, on the Gulf coast
. It was a beautiful day. Perfect for sailing, with a nice 10 knots or so breeze and hardly any chop on the Gulf. Sitting there on the beach, I watch a lovely ketch
coming up the coast. When he gets close enough I realize that, although his sails
are up, they are just flapping in the breeze. On a perfect day like today he is motoring! What the hell does he even have his sails
up for, if he's not going to use them?
This is one of those guys who likes the look of a sailboat, but really is just a motor-boater. I used to have a slip in a marina next to a guy like that. He never went anywhere without his motor running. Sails up or down didn't matter. Wide open water
or going through a draw-bridge didn't matter. He started the motor almost first thing after he arrived at the boat and he didn't shut it down until he was back in his slip and almost ready to go home. He thought I was reckless and a danger
to everyone around me when I would sail into my slip (even though I only did it when the wind
was right and I NEVER had any issue with it).
Now, no offense intended if you recognize yourself here, but if you don't feel comfortable going anywhere without the motor running then you need a much bigger motor--not to mention a VERY MUCH bigger gas tank!--than someone who bought a sailboat because they don't want the noise
and stink of a motor.
On the other hand, if you see a motor as a necessary evil, to be used only when there is no alternative, then you can probably get by with a smaller motor. Of course, you'll also require a correspondingly smaller gas tank. Lots of people have sailed all around the world (still do, actually) without any motor, which makes the case for zero horsepower as the smallest motor you should consider!
So, the general rule of thumb is that you should have about 2 hp for every 1,000 lbs. of displacement
. A Columbia
34, depending on the exact model and year of mfg., will have a displacement somewhere between 10,000 and about 13,000 lbs. That would indicate 20 hp on the low end, up to 26 hp on the high end based on the rule of thumb. But if you intend to motor a lot you should probably consider 30 hp as the minimum. If you are willing to accept the limitations that come with it, you could do without a motor at all, or get by on the 10 hp that is in there.
But you MUST be aware that there are plenty of limitations that come with an under-powered engine! You cannot motor into any significant wind
seas. You are going to be limited on how fast you can motor. There will be times when you want to go that way, but must instead go this way. I would add that MOST boat buyers will consider this boat severely under-powered, and so the resale value is going to be dramatically affected. It should be priced with the expectation that you will re-power (whether or not you choose to re-power is another matter).