(있을) what does this mean exactly?
저는 집에 있을 것입니다 is better
In this case both the 가 and 는 particles work, neither is better, both sentences have the same meaning.
Do they have a slight difference in emphasis? 가 "I am at home" (compared to someone else) 는 "I am at home" (compared to somewhere else)??
The topic particle is used after a noun which is just given.
― Where will you be? ― I will be at home. (저는 집에 있을 것입니다.)
― Who will be at home?/Who will do what? ― I will be at home. (제가 집에 있을 것입니다.)