Learn English – Will be going to get engaged

Using will (or shall) is the proper way to form the actual future tense, and is completely generic. IT can be used in any case in which you wish to refer to the future.

Going to + verb is a shortcut construct that is commonly used in many situations. It is typically used to express occurrences in the near-future.

In many cases however, particularly in colloquial speech, the two constructs are virtually interchangeable.

Wikipedia has some additional notes on usage:

Going-to future is used when the speaker wishes to express certainty about the future based on evidence or fact from the present or the speaker's opinion: "If you do not stop, you are going to be caught by the police and hauled back to jail." "Our houses are going to be swept away by the impending storm." While the "will" and "going to" constructions are often interchangeable, only the "going to" construction can denote former future intention (e.g. "I was going to eat dinner, but decided not to").

They mean essentially the same thing: Are you going home this summer? which is probably the most neutral form of this question.

However Will you go home this summer? might be seen as being curt and could imply that you wish for that person to leave. It could essentially be taken as Will you please go home this summer? but without the please.

Will you be going home this summer? is more inquisitive. It implies that you are merely curious about to their summer plans and you don't particularly care what the answer is.

If this is being addressed to a person that you do not wish to go home for summer you could try asking You aren't going home for summer, are you? which retains the overall neutral value but implies that you prefer for them not to leave.