Is Hajj immediately obligatory for someone who is financially capable, even if they do not own a home? Or is purchasing a home to be prioritized over Hajj?

Allah has made Hajj obligatory upon the one who is able, and that is the one who possesses provisions and a ride, in addition to his essential needs, such as housing and expenses for himself and his children. If the money does not cover these needs, then Hajj is not obligatory until funds exceeding sufficiency become available.