I'm not familiar with the Euro Classic, but the Classic and Deluxe are mechanically the same, the only difference is cosmetic stuff like the chrome and fancier gas tank.
I don't know about the AVL and Electra, but on my cast iron '02 model the electric start is best left for emergencies (i.e. a quick restart at a stop light).As far as I know they are all 5-speeds these days. But that is for the best. I have a 4-speed and the rube goldberg mechnism used to make it left foot shift makes for imprecise shifting at best.Others on the board who have the 5-speed have nothing but good things to say about it.