Your sentence #2 is using would in an old-fashioned way. Here's what Merriam-Webster has to say about this meaning:
*a —used in auxiliary function to express wish, desire, or intent ("those who would forbid gambling")
b —used in auxiliary function to express willingness or preference ("as ye would that men should do to you — Luke 6:31")*
(I included both a and b because I don't honestly see much difference.)
I will do my best to explain why your exercise book chose #2: I think it's because the first part of the sentence is supposed to be a fantasy.
I often think about a big ideal house
They've given us two clues that this is a fantasy: "I often think about," which sounds like daydreaming; and "ideal."
If it's a fantasy, then "will" doesn't quite fit. "Will" implies certainty.