Shame that no other anon chimed in on this.
Really only one way to train cardio
1. C25k, It will suck, espescially with winter coming up, but if you finish the 8-9+week program, then you will no doubt pass the physical at the academy. Being able to run 3 miles in 28 minutes is a starting point, lowering it down to 18 minutes is perfection. However, being able to run 3 miles in 28 minutes gives you the endurance to run 1.5 mile in 9 minutes. At least thats how it is for me.
Now running for cardio and calisthenics for cardio is very different. Your body may be able to handle running for long time since eventually your muscles will adapt and grow to the necessary amount for running. But can your body handle doing burpees or jumping jacks for 10 minutes? Your heart may be able to take it but your muscles may not. Always make sure your stamina for your muscles are on par with your cardio.
Another word of advice I have is if you lift, always do cardio last. This is because no matter how fast, how far, or how long you run, lifting will always be more strenuous. You will use up all your glycogen/energy faster by doing cardio, leaving you jack shit for lifting.
If you can't do pull ups already, start working your way there. Barbell rows, lat pulldown, row machine, negative pull ups. Aim for 5 consecutive pullups. Being able to do pullups also help tremendously with deadlifts.
Final note, do c25k. Leave the house hydrated and ready to go. Wear a mask or balaclava so you warm up the air a little bit more before it enters your body and you dont get the burning sensation as soon. Don't rush the next exercise, ever. If you're sore like a mother fucker, wait a day, wait three even. Eventually your muscles adapt and DOMS will not be an issue. Rest>Form>Workps, my gym has a machine called the jacobs ladder, pretty nifty, I'd use it if your gym has one.