Hi Zach,
In theory, if your screen has indeed come loose, then the only thing you should need is the adhesive to glue it back on.
[product|IF374-019|Apple Watch (42 mm Series 3) Adhesive Strip|new_window=true]
However, it's been my experience that the screens generally don't just fall off for no reason. Most commonly it's because the battery has swollen and pushed the screen off the face of the watch. If that happens, then you need to add a replacement battery to your list of parts. I can't tell you exactly which one to get, as it appears there are differences between the cellular and GPS models of the series 3.
Anyway, you'll want to take a look at the battery itself; if it's at all pillowy or puffed up, that's a sure sign it needs to be replaced. A good, functional battery should have the outer layer wrapped tightly around it like a brick.