Depending on the suppressor.. but I would say wear foam ear protection. Possibly safe in open outdoor areas. Indoors you'll possibly ring your ears.
I shoot suppress and it is so much more comfortable shooting. Plus having weight out front, it helps with muzzle rise.
Neighbors hearing it. Depends how far away they are. If they do hear it, typically it is harder to pinpoint where your shooting from. You'll less likely get a complaint running suppressed over shooting unsuppressed.