Re: 73 Rude 65hp
Start out with a compression check. The OMC triples of that era often have pretty high readings - my '72 65hp Johnson still has compressions in the high 130s. If you get decent and evenly matched compression in all three cylinders, look the motor over to assess general mechanical condition.
Next on the list might be an assessment of the condition of the gearcase and its internal components. Look for obvious signs of leakage and drain the gear oil. Look for signs of water intrusion (milky appearance of the oil) and presence of grit and other impurities in the oil. If that checks out, refill with proper oil type. If the motor will run, try doing so in a barrel and shoft the motor into forward and reverse. Look and listen for proper shifting without noises that might indicate problems internally. While i realize that getting a barrel under this motor might not be easy, its better than running on a muff, if you can do it.
If the midsection, swivel bracket, and transom bracket are in good shape along with the powerhead and gearcase, the two big items remaining are the carbs and the ignition system. Rebuilding a set of carbs usually isn't that big a deal, so the ignition system becomes the next potential money pit.
I rebuilt the ignition system on my motor (its the same as yours) and I did spend a fair bit of money in the process, but I have never been unhappy with the decision to do so. The good news is that aftermarket parts are available through CDI and Sierra, so the cost isn't completely outrageous. Considering that the motor could end up to be a very solid "runner" after an ignition rebuild, I think the money can be well spent.
As always, don't forget the water pump and thermostat. Additionally, your motor has "pressure control" valves in the area of the thermostat. They open when water pressure in the cooling system increases with rpm, regardless of what the thermostat is doing. Those should be checked as well.
Another bit of good news about your motor, is that it is not a hydro-electric shift, as the pre-1973 OMC triples are. While those motors can be just fine if the shift system is working properly, there are a number of parts for them that are NLA. At least you won't have that worry.