Generally I see four options:
- DSLR / system cam (e.g. Canon EOS, Sony Alpha)
- Compact camera (e.g. Fuji Film)
- Action cam (e.g. GoPro)
- Camcorder (e.g. Samsung HMX or Sony HDR)
Before talking about solutions I would propose to think about the requirements. The following topics come to my mind:
- Field of view - Do you want to cover the whole field only, or do you also want to zoom in on single players? Camcorders and compact cams may be limited in wide angle but often offer great zoom. Action cams normally don't zoom at all. DSLR is most flexible with the right objectives, but zooming may not be as easy to operate as with camcorders. Some compact cams stop sound recording while zooming, if that's an issue.
- Light - I suspect it may be a little dark in the gym? So high ISO values and good quality at high ISO values may be important, especially when zooming in.
- Unattended operation - Do you need to leave the cam unattended? You'd probably wouldn't want to leave a DSLR unattended.
- Recording time - battery life time is helpfull, the option to record with power supply may be even better. Also some cams stop recording after some minutes (e.g. EOS 600D after 12 mins HD recording).
- Focus - Many cameras focus on the nearest objects in their field of view. This could be the spectators, not the players. So the camera should offer a deep depth of focus, or the option to manually set the focus.
- Quality - Do you need still images? Which would require you to set a short shutter time. High ISO values would be even more important then.
- Display - Where do you want to watch the recordings? If directly from the camera, you'll need an HDMI output or something similiar. Some Camcorder even offer an integrated beamer, so you could watch the recording directly in the fitting room without any further equipment. And you'll probably don't want to show the whole game, just parts of it? So you might want convenient fast-forward/rewind features. Some cams even offer very limited postprocessing capabilities, so you could cut away the uninteresting parts of the game.
A tripod may definitely be a good idea, but it needs its space. A smaller device to fix your camera to e.g. a fence may be even more appropriate (e.g. Gorilla pod). If you go for a tripod make sure it's high enough and strong enough to hold the weight of your cam.
Memory Card - it must be fast enough. If it's not, it may stop the recording in the middle of the game. How fast? Depends on the video format of your recording.
Assuming you don't want to zoom in and you want to leave the camera unattended somewhere, I tend to agree with AJ Henderson: An action cam might be the best way to go. Add a gorilla pod to fix the camera somewhere, get a big and fast memeory card and make sure the recording/battery life time fits your needs.
For more sophisticated use cases a Camcorder with integrated beamer, power supply, strong wide angle, high ISO plus a tripod may the right choice.