As a Webmaster this will probably the most important aspect that you are intrested. Has all your hard work been seen by those that it was intended. I personally view the visitor statistics for the Village Hall webisite on a daily basis.
I also feel that the whole subject of Statistics is a little too "Social Media". When starting out with a website the first thing that a budding web designer would do would be to out a page counter on their pages. I know, I did this! The "Social Media" aspect of this now, 20 years later, is that it is too easy to become obsessed with getting "likes".
My recommendation is to not worry too much about the actual statistics, initially most of your visits will be your own and from those that you have asked to check yuur pages. The real advantages and benefits of the site statistics is when you have already gained an audience and you can then use that information to fine tune your site. It is a bit of a "chicken and egg" situation.
Granularity of Visitor Location
One of the most important things that you want to know is where your pages have been accessed from. This along with what pages were viewed and ideally where the visitor entered your site and where they went.
A long time ago Google Analytics offered this information. Sadly, this information proved to be too valuable to Google to freely reveal this to webmasters and it is possibly available if you subscribe to some of their services as a business, but this information is largely suppressed for the Internet user and the average webmaster.
Wordpress.com offer Web Statistics as part of their standard interface but this only gives the country that the visitor accessed yur site from. This is not much good if you are trying to ascertain who is visiting from your village! The Village Hall website gets a pretty much even spread of visits from the UK and China. I am presuming the UK visits are local ones and the Chinese are just "fishing trips". The recording mechanism on the Wordpress interface is pretty instantaneous, when I click on the site by mistake it shows immediately.