Fitness is really a sliding scale, so there won't be a one size fits all approach to it. But with that said, you really need to set a goal to make a difference to your own "fitness" for paintball.
That might be something as simple as "I want to lose 5 kilos so that I can get up and going quicker in a game" or it might be as far down the road as "I am fit and strong, but now I need to improve all my reaction times and sprint speed", both of those are going to have different approaches (the first could simply be to stop smashing down service station burgers on the way to events / home from work).
If it's exercises to specifically emulate playing paintball, think about things which include a relatively light weight (compared to your body) but require you to move it around and away from your body. (think dumbell shoulder press / pec dec with smaller plates in your hands / weighted lunges)