I can't comment much about paintball. Last time I took part in a paintball I took a shot in the head which was incredibly painful!
Showing a timer should be fairly straight forward. To create a view of the battlefield then I'd suggest something like pygame zero, which makes creating a GUI easier than using traditional GUI environments.
For the screen I'd suggest one of the AdaFruit TFT touch screens.
Personally I like the 3.5", but you may prefer a smaller one such as 2.8" if putting it your wrist. Although not sure how rugged these are as they may get damaged through rough use.
You can get the TFT screens from several Raspberry Pi suppliers.
For battery - do you really mean 2500mAh? That is pretty small and may not be able to provide enough power for running the Pi and TFT simultaneously. 25,000mAh would give you a good battery life and whilst they are fairly big would fit into a pocket. Or you could try something around the 8,000 to 10,000mAh range which could give you a smaller battery size if required.