Light aircraft pilot landed safely at HWD after receiving a low altitude alert from ATC on the approach.

Narrative

Before the flight I had thoroughly briefed the weather; approach and the airport. It was MVFR with a thin layer of overcast. Although I had never been to HWD; I fly almost daily from ZZZ (and fly over HWD during my typical approaches to ZZZ.) I was being vectored for the RNAV 28L approach from the NE via a series of right turns from 5000'. After a number of turns to the right; I was instructed to turn to 260 and join the approach course at 4500'. I was then issued a traffic advisory for traffic at 3500'. Shortly thereafter I was instructed to descend and maintain 4000'. At this point - for some reason unbeknownst to me - when I selected the 4000' altitude and commanded VS (Vertical Speed) down in my autopilot; the autopilot began to climb. I verified that all settings and inputs were correct. I decided to disengage the automation and hand fly the approach. However; given the traffic and automation distraction - and the fact that this was the first time I'd flown into this airport - I didn't have full situational awareness of my position relative to the final approach fixes. (Note that I'd never heard a call like 'expect vectors to <fix name>' from ATC). As I tried to determine the altitude that I SHOULD be at I flew through the inbound approach course. I was then issued an instruction to 'turn right to 310 and intercept the approach course.' I was then cleared for the RNAV 28L. Approximately 45 seconds later I was issued a 'low altitude alert' and that 'MVA in my area is 3400'. I was then asked if I was on the RNAV; which I confirmed; and was told to contact Tower. Shortly before the alert; I had broken out of the clouds with the field (and ground) in sight. I did not receive any TAWS warning from my onboard system. I had considered breaking off the approach and asking for vectors to re-sequence; but because I had the airport and ground in sight I felt it was better to continue in what was basically a visual approach. And I was at the proper altitude for the next inbound fix.In retrospect I think there was a variety of factors at play. Had it been worse IFR; I certainly would have immediately abandoned the approach. The 'MVA' call confused me momentarily because I was at a fix that was below the MVA. I did descend below minimums at one of the intermediate fixes. Lastly; and most importantly; next time I'm at an unfamiliar airport/approach; I will ask the controller to which fix I'm being vectored so I can have a 3-dimesional picture in my head and not just rely on the automation.