Set up your 240 gal by putting water, treat it, to take the chlorine out and other harmful elements. Put heaters. Make sure the original temp from the old tank can be almost the same as the new tank.
Before you start draining your water, put the old tank's water to the new tank. Since you have 100 gal of old water, use it. just fill up the new tank up to 120 gal and the rest from the old tank. do not throw away your old water. it is useful, one it will help you go to the temp you wanted to, second the aged water will help for the fish to avoid stressful situation.
If you have big bins, put all the fish in the bin, with the old water. have some drip tubes to acclimate them from the old to the new tank.
once the desired temperature has been reached, start acclimating them.
use your old filter (canister, wet/dry, HOB) on the new tank. You don't need to cycle it. Just treat the water before doing anything (the new one).
Transferring them is up to you. if they are small fish, use a small bucket, scoop them out and slowly release them.
If you have a big fish, I would get a big bag and slowly release them.
if you don't have any big bags.. i would net them out and put them in right away (after acclimation).
I hope I made sense.
Stress coat helps for me when i transfer fish... but that's my opinion.
