Should he go for an interest-based mortgage if that is cheaper than renting?

Dealing with riba (interest, usury) is haraam according to the Qur’aan, Sunnah and scholarly consensus. So it is not permissible to do that, no matter how great the need. The fact that a person may need a house or car, or to get married, or any other need, does not give him the excuse to do something that Allaah has forbidden. The Muslim has to fear Allaah and remember that He is always watching; he should prefer the Hereafter to this life. If he finds someone who will lend him the money then all well and good.  If he cannot find anyone who will do that then he could borrow from a Muslim, taking a loan with no interest involved. If he cannot find anyone to lend him money then he should be patient in the hope of earning reward. Whoever gives up something for the sake of Allaah, Allaah will compensate him with something better than that.