When you calculate corrections, you will get both types so you can decide for yourself. Linear filters are named ie xxx-hyblin-L.wav and minimal filters are named xxx-hybmin-L.wav. To be exact, what is called linear phase here is in fact a mixed phase correction, because due to the length of correction (taps number), the phase is not completely corrected down to lowest frequencies.
Pre-echo artefacts cannot appear with minimal phase filters but note that the linear phase correction is calculated so to avoid any risk of pre-echo. Generally, it is better to start with minimal phase correction and compare afterwards with linear phase.
If you have 2048 taps or less for your FIR processor, it is more efficient to use minimal phase correction instead of linear phase.
The audibility of phase is often discussed : large phase distortions are easily heard but common ones such as phase distortions of crossovers or group-delay of bass-reflex or other kind of boxes are not so easy to perceive. But David Griesinger has an interesting theory about phase distortions, ie have a loook at this paper.