You need to start with creating a spreadsheet with some sample data. You will create a sheet for each entity. The entities that I see in your description are:
Item (aka Equipment)
and maybe Reservation (if more than one person can make a reservation for the same “Place”
As you build the Spreadsheet structure think about how entries in one sheet are related to a single row in another sheet or multiple rows in another sheet.
I would say that each row in the Reservation sheet would have a link back to a User, a Place, and an Item. Places most likely would have a link to the Items available for that Place.
Bottom line it seems pretty straight forward on the surface but most likely is a pretty complex application. Especially when you think about the need to keep some kind of track of how many users have already made a reservation an then how many slots are left for more. Then you have the issue of only having one set of 25lbs kettle bells at a specific Place. It can get complex real fast.