The best place to find out about the crime rates in your new area is to visit the City of Richmond . The web address is http://www.richmondgov.com/Police/CrimeIncidentInfo.aspx.
I never leave anything visible in my car, it is asking for trouble and I always lock my doors. Living in a city requires extra diligence but fearing for your safety is not necessary. I have personally lived in pretty much every area of town and have never once been burgled. I have had my car messed with but that could just be drunk college students being college students. You can certainly get more piece of mind with having an alarm installed and getting renter's insurance. Good luck, enjoy your new casa!