I had a friend who got shot in the chest while chasing a suspect. He was wearing soft armor and the BG shot him with a 380.
He said it felt like someone hit him with a baseball bat, but he surived.
Those US PALM carriers at FF are a good entry level PC to have. Another good choice for low profile would be a BEEZ combat soft armor carrier.
Despite the unwanted comments here , get what you want; SAPI plates can be had on CL for a resonable fee; I recently saw a full set of ESAPI paltes locally for $100-, that is a hell of a deal.
And depite what others here say, if the SHTF in Mpls like it did in Ferguson MO, any ballistic protection is good, especially low profile stuff like the BEEZ taht can easily be concealed under a shirt.