hoeuiga kkeutnago naseo baro jibe gayo.

-고 나서 is a connective ending that explicitly marks “after doing something.” It links two actions in sequence, emphasizing that the first action has fully finished before the second begins.
• 회의가 끝나고 나서 바로 집에 가요. = “After the meeting ends, I go straight home.”
By contrast, -고 alone can simply join verbs without stressing completion:
• 회의가 끝고 집에 가요 is ungrammatical—if you want to link finish+go, you need -고 나서 or at least -고 with full completion implied.
• 회의가 끝고 집에 가요 would sound odd; always say 끝나고 집에 가요 if you’re just chaining events casually.

바로 means “immediately” or “right away.” In Korean, adverbs like 바로 typically come just before the verb or adjective they modify:
• (…끝나고 나서) 바로 집에 가요. = “(…after that) I go home right away.”
This placement highlights that “going home” happens without delay.

In Korean, the simple present tense (-아요/어요) often describes scheduled or expected future actions—much like timetables in English (“The train leaves at 5”). Here, going home right after the meeting is a planned sequence, so 집에 가요 works perfectly. You could use 갈 거예요 for emphasis on intention, but it’s not required: • 회의가 끝나고 나서 바로 집에 갈 거예요.

집에 가다 literally means “go to home.”
• 집 = home
• 에 = location/direction particle, marking the destination of movement
Putting them together: 집에 가요 = “(I) go to home.”

Yes, -자마자 also means “as soon as.” It stresses that the second action happens the instant the first does:
• 회의가 끝나자마자 바로 집에 가요.
Nuance: 끝나자마자 is more immediate and can’t have any delay, whereas 끝나고 나서 바로 allows a very brief, possible moment between actions (though “바로” still implies little to no delay).