"....allows new squash leagues to be downloaded approx. every 8 weeks" Do you mean that members can download files from the site, or do you really mean that new tables will be uploaded?
I ask, because it makes a big difference. If files are going to be put on the server for download nothing could be easier, but if files have to be uloaded by members it gets a whole lot more complicated. I am in the process of designing a site for a tennis league, and in that case they want to be able to allow club officials to enter league match results on a weekly basis. This involves a good deal more work on my part, and is consequently more expensive from a design point of view.
If you simply want to upload files to the server for members to download it's an easy DIY job. You'll obviously have to experiment with whatever software you decide on, but we're here to help when you get stuck.
I'm confused by your last question "Would we need to have it hosted instead of using templates?"
All websites have to be hosted on a server. templates are simply that - ready-made page layouts, into which you insert your content before publishing your site to the server. As for Pipex allowing files to be downloaded - they have no say in the matter. Whenever you view a web-page (on any site) your browser is downloading the html page files and displaying them for you, that's how it works. If you want to have other file formats avalabe for download - PDF, or Word documents for instance, you simply put them in a folder on your server space, and provide a hyperlink to them on your site pages. The visitor clicks the link, and his/her browser does the downloading.