In my opinion, you would probably get the best results if you were to do the bodyweight exercises in a circuit. Start with a plyometric move like squat jump high knees and then move on to your standard bodyweight movements such as push ups, pull ups, pistol squats, etc...If you would like to build more power and strength then you will eventually need to invest in a gym membership or some heavy implements of some sort. You can't really build strength without exhibiting strength and to do that you need something heavy.
Since you are young I am assuming that you don't have a lot of money to spend so I would recommend collecting some large stones, a tough bag that you can fill with sand, sections of logs, etc... A lot of the time you can find stuff like this for free on Craigslist or being disgarded at logging sites, construction sites, demolition sites, etc... When I was training for strongman I acquired a lot of good training implements this way.
You can use odd implements to do pretty much any movement that you would do with a barbell and they are convenient for using during weighted carries and weighted drags which I definitely recommend you use in your training.