Am I limited by the pKa value of an weak acid when preparing a buffer solution of it (and its salt)?
If I was to make an acidic buffer system with the ph of, for instance, 4, would I be limited with my choice of weak acids?


Yes you are limited to weak acids that have a pKa of +/-1 of your desired buffers pH value. This is a rule of thumb used in many labs.Some theroetical background is quite nicely explained on wikipedia wikipedia#buffering  capcacity.

This reference also includes some useful equations related to buffering capacity.