ISBoxer.com

I only have as an option the no BN 64bits launcher, and can't find a way to automatically login.

Also kind of curious about this "order" you should login mentioned in the quick setup tutorial.

The order relates to your character set, and which character is in each slot.
Depending on your mapped keys you are using, it may not make much difference for D3. If you have mapped keys that send actions to a specific character, or a specific slot, and you don't have the expected character in the slot, then you will have the wrong character doing the wrong thing. For D3, which seems to be mostly broadcast everything, I'm not sure it matters.

Unless the game or it's launcher provides a means to automatically log in, then you cannot. For D3, there is this guide on the WIKI (I think it is still valid) http://isboxer.com/wiki/HOWTO:Autologin ... Battle.net.
You are mainly interested in the part under "The game launching process", but, if you had to add D3 manually to Inner Space, then you may need to Add Game, and point to "Diablo III Launcher.exe", and then update the characters to use the new game profile.