"I go home."
Translation:저는 집에 갑니다.
With 가다 and 오다, 을/를 can replace 에 for emphasis. "저는 집을 갑니다." is also correct.
In this case saying 집에서 would be "I'm going (somewhere) from my house"
까지 is up to. 에 focuses on the destination whilst 으로 is about the direction. In this specific sentence, 에 is better, but 으로 could be used synonymously, but in some cases they are totally different.
- 자동차가 앞(front)으로 갑니다. (The car is going forwards.)
- 자동차가 앞에 갑니다. (The car is moving in front (of me).)
You could probably use ~까지 but it's less common in my experience. It's more used if you're asked where you're going. ~으로 sounds a bit different. In English you would say it like "I'm heading home." which technically could mean you're going in that direction but not necessarily straight to home.