"Will have" refers to an event in the future that precedes some other event in the future. "By the time the police arrive, I will have hidden the evidence." At some point in the future the police will arrive. Before that time, but still after the present time, I will hide the evidence.
"Would have" refers to a past hypothetical. It is used when you want to say that an event didn't happen, but that in some alternate universe where conditions where different, it did happen. (Okay, that's an odd wording, but I'm struggling how to express the idea without using the words "would have". To say, "would have" refers to something that would have happened ..." probably doesn't help. :-) Like, "If Sally had passed the test, she would have gotten the job." Sally didn't pass the test and didn't get the job, but if she had passed the test, then she would have gotten the job. "Jack would have won a fair contest." Jack lost the contest, but if it had been fair, he would have won. (Or perhaps there never was any contest, but if there had been a fair one, he would have won. Depends on context.) The condition doesn't necessarily have to be spelled out in a simple IF/THEN construct. You could say, "Mr Smith died before I was born. I would have liked to have known such a man." In this case the condition is clear from the context: if our life-spans had overlapped. It could certainly be more subtle.
I'm struggling to think of any other use of "would have". If another poster here thinks of one, please feel free to shout it out.
You could not use "would have" instead of "will have" in the above paragraph, because (a) there is no condition on Jack selecting the living quarters, and (b) even if there was, "would have" is used for past events, not future events.