~아/어야겠다

If you want to say something that is very likely to happen, use ~어/아야겠어요. How it differs from the rest (forgive the non-exact translations):

"I will do it" (ㄹ)게요 / ㄹ거예요
"I'm probably going to do it" ~아/어야겠어요
"I am planning to do it" ~려고요
"I guess I'll do it" ~겠어요
"Seems like I might do it" (ㄹ) 것 같아요

It feels like a cross because ~어/아야되다 and ~겠다 probably because that's exactly what it is. It's hard to express the exact same feeling in English but it indicates a 75%-80% chance that something will happen. It's really likely and you're planning on it. You have a strong will for this thing to happen.

Examples (with non-literal English):

이제부터 저축하야겠다
(That's it). From here on out, I'm going to start saving more money.

옮겨야겠어요
I'm really going to move soon (I gotta get out of this place).

내일 일찍 나가야하니까 지금 자야겠어요
Since I have to leave early tomorrow, I'm probably going to go to bed now (Just FYI).

들어야겠어요
I'm definitely going to listen (cause I really should you know)

술집에 발을 끊어야겠어요
I gotta stop going to the bar so much...