This is really simple. It will take you like minutes to do this. Just go to this page and register. This is my choice not because it has nice fancy counters but because it uses pure HTML counter. There
are a lot of other counter providers but the problem is that most
of them use JavaScript and it is not fully supported by GPC yet, so
that is difficult to do.
There are a few features that you can use, concerning different properties of your visitors like what page they came from, what country they are from, their browser, OS, etc. etc. When you register you will be give two pieces of code: one for the visible counter that shows how many visits you have had and the invisible counter that you can place on a page and track the number of visits to that page without having the number of visits shown on it.
My advice to you is to place the visible counter on the homepage, and create other projects and place the invisible code of those projects on other pages so that you track the number of visitor, but you also track the number of visits to your other pages. You should also only have the unique visitors counted, and not just page loads. That way you are really counting visitors and not just the number of times your page has been accessed.
I have seen that many people use this:
"You are the " [visible counter code here] " person to visit this site." You might consider doing that.