In my experience, long-term endurance plays little in any paintball role. Games typically don’t last that long and any movement that you’re doing will be at max a 10-15 second sprint. After which, you’ll crouch or stand for a few minutes while shooting at someone. A more important thing to address would be your overall fitness, more specifically your diet.
First and foremost, attacking your diet is priority. The old mantra “calories in < calories out” still holds true, but aiming for a proper macronutrient ratio is ideal. Switching to a high protein and mid to low carb diet will help accelerate fat loss in the beginning. Contrary to what most people think or choose to believe, exercise will do little to nothing for your health if you are eating poorly. However, I do not mean to rule out the importance of exercise. Aside from the benefit of improved cardiovascular health associated with both weight lifting and cardio (yes, lifting does improve CV function), exercise will obviously increase net calorie expenditure and contribute to fat loss while adding lean muscle. In regards to sprinting versus sustained runs, honestly do whatever you can for now.
Diet > exercise
You’ll notice with a revamped diet an increase in energy levels which’ll also help with your exercise goals. I recommend a balanced workout regimen of both lifting and activity. A very good program I have seen used with great results is a typical 3x weekly full-body lift with 2 days of cardio interspersed. Full body lifts accentuate more overall body fitness than targeting single muscle groups just to blow them up while increasing your HR more and can mimic a cardio-lifting routine much in the way that CrossFit works.
I hope the info serves you well. Good luck, get to it, and you always have paintball to help with the cardio.