Strafe using A and D and use your mouse to turn so you don't look like a newb, this frees up Q and E keys, with shift, alt and ctrl, that gives 8 extra keys.
I unbind the scroll wheel from zoom and use ctrl + up and down to handle that. That leaves the wheel up and down, with Shift and alt to bind for abilities you will want to spam like interupt. That gives another 6 keys for binds.
I have G500 mouse, logitech is awesome with the mouse wheel that tilts, I assign those as keystrokes then use [ and ]. With modifiers that gives me 8 more keys.
This mouse has 3 thumb buttons on the side, which gives another 12 keys with modifiers.
The mouse also has 2 more buttons beside the left mouse button (default is sensitivity adjust which I never use), I use one of those for vent to mute my mic, (I use voice activated).
With the modifiers Shift is my most used one, followed by ctrl and alt. I usually group similar abilities on a button then add modifiers, taunt is mouse wheel tilt left and aoe taunt is shift mouse wheel tilt left. If you plan to play alts like I do copy the location of similar abilities on your keybindings to help learn them all faster.
I am only level 33 on my vanguard and I keep moving keys around, the relearning process is annoying doing that but I am getting a better feel of what I should be using all the time.
The mouse I use.
Gaming Mouse G500