I've played this game for a long time at a pretty good level. I've never moved away from the default keybindings though. I've once tried attack move on mouse 2 once, moving the normal move command that was on mouse 2 to mouse 1, but I think I ran into issues where I couldn't click on the minimap or store without my character getting ordered to move to whatever was behind the menu or map. My line of thought was that I would orb walk (stutter step/whatever) by alternating left and right mouse clicks. Sounds like it makes sense, but a change like that takes getting used to. To be honest that increases the complexity of what I need to do with my right hand significantly so it probably only made sense on paper. Besides now I don't find hitting A to attack move in between right mouse clicks hard at all. This game isn't very mechanically intensive compared to something like starcraft (I never really played it); don't need to do a lot with the keyboard on most champs so moving attack move to the mouse seems kind of inefficient I thought.
Anyways I think you need to manually edit the text in the keybinding config file to set it up the way I did. That's probably why the game interface wasn't expecting my configuration and I couldn't buy items in the store without moving away from the fountain or pan around on the minimap without having my character run to the corner (very very annoying). This was a while back though.
Sorry about the rant.
I just use 'A' to attack move sometimes. Very used to it. Hard to explain. It can be useful especially when your enemies walk into a brush with no hp, but sometimes it can mess you up and cause you to attack something you didn't intend if you're not careful when you use it. I mostly use it when kiting enemies backwards. And yeah, you just have to know your attack speed and keep your rhythm.
If you're not orb walking, that's lost efficiency either as ranged or melee. Auto attacks go off at a certain point, but not necessarirly at the end of the animation. Giving a new move command once your auto attack is legit increases your mobility. Also orb walking allows you to better control your champion. I mean... if he has a command to attack something, he'll only go as close as necessary- the very edge of his range- and stop there, making it very likely you'll not be in range if your enemy simple moves one inch backwards. Imagine playing a melee champion chasing a fleeing target. With orb walking you'd be able to get in front of the way he's going (so if he flashes for example you need to cover less ground), smacking him the instant it's possible everytime... instead of trailing behind him at the edge of your range, needing to catch up again when your auto attack is ready again.
Now THIS is awkward LOL