The games do have a sort of “development” path from 41 to 42.2 to Anniversary to 1940 (Europe / Pacific through to Global).
Taken in that order the rules for each step build on the ones beforehand, adding various elements that then apply to future steps. When I teach others to play the game I will follow that path.
None of which precludes you deciding to miss some steps out. Anniversary is felt by many forum members to be the best A&A variant and jumping from 41 to Anniversary is certainly doable for those who have taken to the game.
1940 (especially Global) is probably the favourite of even more forum members. However, jumping from 41 straight to 1940 will be harder and might prove discouraging for those less dedicated to the A&A format.
Forum members are, of course, A&A addicts :-D and the very suggestion that anyone could possibly prefer less complex variants can be beyond understanding for some. But if I guess at my “teaching” statistics:
Taught 1941 - perhaps 25, of which 9 continue to play regularly or occasionally
Moved up to 42.2 - 6, of which 3 continue to play regularly
Moved up to Anniversary - 3, or which 2 continue to play regularly
Moved up to Global - none.
So your choice may depend on the extent to which those you will play are dedicated to the A&A format.