Download page or Download Manager?

I am creating my first website using WordPress. I now have a page on my site with a download for a program I wrote. This is a page which offers users a choice of a .exe file or a .zip file to download. This is for a free-trial of the program.

It has occurred to me that once I go live with this site I will have no idea how many people are downloading the program. In searching the net for a way at least to count the downloads, I have discovered the Download Manager plugin. So it would seem I need to ditch my download page and go with the Download Manager plugin. Or is there some way I could modify my existing page to count the downloads? Or perhaps another plugin would be more appropriate for my situation? Basically what I need now is to be steered in the right direction before I change my site. So what do you suggest? If possible I would like to retain the choice of two files (a .exe or a .zip) currently on the site.