If you can perform a full burpee (from standing to the floor) then the benefits are huge. You can also scale and go from standing to plank position or use a swimming pool (stand in the pool near the edge, jump onto the ledge and then back into the pool and go into squat position underwater).
You will be getting a shitload of hypertrophy with all this bodyweight exercising though so you'll look shredded if your body fat is low.
Squats easy for you? Try pistol squats.
For a year I've been exercising in my backyard with a podcast in my ears, maybe during a group phonecall for work, while thinking between programming sessions, etc.
Now I realize that 100% of these people are full of shit. I got jacked. Whenever I've mentioned this to someone, they'll say something like, yeah but you can't get as big as $bodyBuilder, like Ronnie Coleman.
The truth is I think very few people have actually tried a serious daily bodyweight regimen. Most people don't have a reason to try, they just go to the gym if they want a daily workout. And then we, including myself, have the human tendency to regurgitate ideas we've heard from others rather than from personal experience.
This is why I chose resistance training - the gym is on my way to work and I am willing to spare about an hour and a half daily to fitness. My research indicated I'll get better results with that time at the gym lifting weights than body weight training.
It can also be less efficient though in the sense that it can sometimes require a pretty big jump in both strength and technique to go from one progression to the next, so you can get stuck for awhile. With weights you can of course just keep adding a little bit more. But the plus side of this for bodyweight training is that apart from just strength, you also get improvements in muscular coordination, balance, flexibility, and body awareness.
You don't really have to choose though--you can do both! They complement each other quite well.
But anyway, what does that have to do with comparing burpees to squats/push ups? :)
One arm push ups are way harder than normal ones. It's not something I've tried working on yet myself, but I think you build up by doing things like archer push ups with the other arm assisting less and less until you don't need it anymore.