X-wind takeoff and the a/c wants to weathercock into wind. Downwind rudder is applied to keep on centreline. Into wind aileron is applied as has been said. B737 rotate and it wants to roll off the wind. Keep wings level with even more aileron. But hang on a minute; guess where the rudder is; encouraging the a/c to roll off the wind. The B737 has a roll off tendancy anyway; keeping the downwind rudder on during rotation increases this tendancy. Thus, why not slowly release the rudder during rotation so that it is off at lift off, allow the into wind aileron to cock the nose into wind - which is what you want to do to hold the centreline - and use the aileron to keep wings level all the time. Holding track for centreline in HDG SEL will depend on what HDG is set on takeoff. Some airlines demand RWY HDG (zero drift), some airlines allow pilot discretion to pre-set a drift HDG. As you lift off in the former case the a/c should be tracking the centreline, so why not 'gear up match HDG'? The F.D is then correct and Bob or Hairy Dick is your uncle.
Trying to make it too scientific and exact is not perhaps what piloting is all about. Feel and intuition are also part of the game. Making it less difficult is also up there.