Research is conflictual when it comes down to the type of shoe you wear, and the associated injury-rate.
Despite this fact, it makes sense to pick up a shoe that matches your foot type. Flat feet? Try the motion control type. High arch? Go for the neutral type. You obviously do not want to “aggravate” an existing condition.
Some good quality studies have randomized one of the three shoe types with one of the three foot types. Inc conclusion, the authors found a very similar distribution of injuries among all different groups.
What does this mean? Basically, you want to go for a shoe that matches your foot structure - common sense - but also, and maybe even more importantly, that feels really comfortable. Do not focus on the price too much. Try it and decide immediately if it fits you well, or not.
Statistically, most people have an inward forefoot flare after landing and should be fitted for a semi-curved or curved shoe.
A final note about barefoot/minimalist shoes running: there is, to this day, no evidence for benefits towards injury prevention. Some studies even showed an increase in the injury rate. Running with these shoes usually mean a change in technique - forefoot strike - that decreases the loads on the hip, but increases the loads around several foot areas. You want to be very progressive and careful when transitioning from regular to minimalist shoes.