I don't have a choke cable on my 240 with three webers. I was looking for some information on what cable to use and the best way to hook it up.

Got it started for the first time the other day, the carbs were a bit gummed up, pulled out the main and secondary jets, they were green. Don't think the accelerator pump circuts are working so I'll have to pull those apart and see what's going on with them. One more question on the fuel system - the gas line flows through all the carbs and out the third one back to the tank I think. Does it have to flow like this or can it end on the last carb? Looking at setups on some websites that sell them it looks like they don't have a two way connection on the last carb.

Ending at the last carb is called "dead heading" the fuel line, and it works fine, but it is hard on the pump.

I would suggest you don't use the choke, but if you do the way that I seem to remember it being done was by using one of the SU choke cables and stripping the sheath off of the cable, then running the cable through the arms on the carbs and trimming to the correct length. Most people with triples just use the accel pumps to squirt a little fuel in there, fire it up, and play with the gas for a minute until it will idle on it's own.

Sounds like you're on the right track as far as cleaning the carbs out. That will obviously make a big difference in how it runs.