yes, you should bulk. why would you cut if you are skinny? lol
how long, you ask? until you look in the mirror and say
"im getting fat; i should cut weight and get rid of this blubba"
You can't just work your chest and expect to get results. Look around and read up on workout routines here or elsewhere to get an idea of a full workout. If you want to build muscle, you need to engage your body more than what you've listed.
Google 'full body workout' or search for it on this site. This type of routine will have you working your entire body during each workout. Long story short, do some reading, get an idea of a full routine then post back with what you're thinking.
Regarding the bodies, a bulked body just means that there's some significant muscle on it. It may or may not have a lot of fat. A cut body will not have a lot of fat, but may have varying degrees of muscle. Seen a huge dude with a big belly? Bulked. Seen a huge dude with ripped abs? Bulked and cut.
Sorry I was just wondering about my chest workout but heres my full workout
Monday: traps/delts
Tuesday: legs
Wednesday:chest/triceps
Thursday:biceps/back
Fri-Sunff