Trying to get lean

I'm a 20 year old college student trying to get into shape. About 5'11, 230lbs
I recently checkout a boxing club said to have hour work outs where based on how much you put in you could burn about 1,000 calories in an hour

And I was curious if that type of workout would be a more rewarding option then say going to the gym and doing tons of reps on machines at half my max(roommates idea), treadmill, etc.

my current physique

what i'm working towards(lean, athletic type)
The thing about the guys in those last two pictures is that there is a fair amount of muscle on them. People new to fitness think that they can just lose their fat and look like these guys. It doesn't quite work like that. You're going to have go diet, burn the fat, lift and eat to put on the muscle, then diet while lifting to burn the fat back off. Not to mention, you're looking at a strict routine if you want to look like that. I read an interview with Jason Statham once where he talked about having to keep a small notepad in his pocket at all times to track every last thing he put in his mouth every day, including gum. Not trying to sound grim about the whole process, but people aren't completely aware of what kind of work really goes into looking like that. It's not something that's going to be a "Beach body in three months" kind of thing. Don't get discouraged 6 months into it. There are a few guys here that are always more than willing to give good advice.
Burn more calories than you consume. Start a well-balanced base fitness routing blending cardio and resistance (bodyweight or weights). There is some great info in the bodyweight exercise area of this forum if you want to avoid the gym. Train hard but have fun.