It seems that both Bohr and Rutherford assumed circular orbits of electrons around the atom. But why did they do so, instead of assuming e.g. elliptical orbits?
It's a common assumption for planetary - ie central Newtonian field - models to consider the orbits to be circular. I don't think Bohr or Rutherford ever believed in circular orbits for electrons, but rather decided to use a circle to describe an orbit they believed was elliptic.
Rutherford-Bohr Model use the planetary system as an analogy, where the movement is in fact elliptic but can be approached by circular paths. Using circles allows you to handle discrete set of radii rather than discrete areas for the movement, hence making the description of orbital jumps easier, but I don't believe Bohr or Rutherford had any fundamental reason to believe the orbits where circular. Check the maths (it's an exercise we did in uni) and everything works fine for fixed areas and elliptic orbits. Actually modern view of the ground state of an electron tend to represent it as orbiting in a path of nil-area, so you would need elliptic orbits if you want it to have a speed. I believe Sommerfeld published a more refined classic model for electrons using elliptic orbits.
Short answer: they wanted to keep it simple