Build a bigger chest and lose belly fat at same time?

I'd just go on a cut and make sure to lift weights twice a week and after your belly gets small enough, you can try to add more size. You may find after your cut though, that your chest will appear bigger

 

Either way is fine. Though there's really no good reason to focus 100% on one over the other. You absolutely can do both.

 

Tons of Push-ups and core exercises everyday, and eat clean. You can achieve both together.

 

It depends on training experience.

If you're relatively experienced, it's not going to happen. If you're a noob to resistance training, you can do both at the same time.

 

Why are you particularly keen on building a 'bigger chest'? :think

 

Do the hypertrophy stuff first - dont cut and then try and gain mass you'll just lose the cut