I can tell you that you *definitely* should check out the neighbourhood.
There are no new IP addresses so whenever you take out hosting you are being assigned a used IP.
I was ignorant of this when I moved to a new server taken out by a family member and found that mail sent by the server was blacklisted due to the activities of the people who had used it before.
An agency I work with took out a new server for a hobby site only to find it deluged with spam traffic due to thousands of links built to the IP address by the spammers who had owned the server before.
These were both reputable hosting providers (or so I would have thought). If I ever take out a server myself I will not go with a company that doesn't issue a guarantee that the IP has a clean bill of health.