Please note that the term "finite wire" needs to be taken with a grain of salt. You can't have current (at least, not steady current that are usually used in intro physics classes) in a finite wire. It needs to be closed somehow for there to be current flow.
The RHR is useful and can be easily used for a straight wire segment and also for a loop wire. You line up your thumb with something that you know is flowing straight, OR, you curl your fingers around something that you know is "curling".
This means that for a straight wire segment, current is flowing along the wire, so you line your thumb along it, and the curl of your fingers shows the direction of the magnetic field. For a loop of wire, you curl your fingers in the direction of the current flow in the loop of wire, and your thumb shows the direction of the magnetic field.
RHR is useful if you know how to use it properly.
Zz.