I would say the precision needs to be in the 0.1 degrees range.
Basically let's say I have to aim at something with the camera on the first position, do a specific motion and come back to the first position: I want to be able to come back to the first position as closely as possible.
Obviously, the precision will also depends on how close the object I am filming is from the camera or on the focal.
If a stepper can do that, then that's great 
Regarding the budget, I have not decided yet but I won't go for more than £100 by motor I think.
Thanks for the links!
Cheers