Circular Orbit in a spherical potential

If we some point mass of mass $M$, in a spherical potential given by $$\Phi(R,z) = \frac{GM}{R},$$ then under what condition would we get a circular orbit, supposing our initial radius from a central body is $R_0$.

Personally, I can't see an elliptical, hyperbolic or parabolic orbit coming out of a spherical potential. How would the total energy and or the angular momentum of the body have to be changed for a circular orbit to arise?

This was left as a remark in one of my old lecture notes and I can't figure out why it would not be circular and what consequentially what conditions make it circular.

A circular orbit occurs, if the test body has the "right" velocity: $$v_\text{circ} = \sqrt\frac{GM}r$$ If the velocity is less, the body will enter a non circular elliptical orbit or fall onto the central body (if it has a non zero extension). If the velocity is higher, the body will enter a non circular elliptical orbit or escape in a hyperbolic orbit.
Planets and comets have elliptical orbits. If the velocity at any point (eg initially) is not tangential, the orbit will not be circular. If the velocity is tangential but $\frac{mv^2}{r}$ is not equal to the gravitational force $G\frac{Mm}{r^2}$ then the orbit will not be circular either.