Don't base it off if they give you a conditional offer or not. If a university gives you an unconditional offer, alarm bells should start ringing immediately. If York is your second favourite university, and Warwick is your first, then firm Warwick and insurance choice York. That way, if you don't get the grades to satisfy Warwick, you will be going to York no matter what.
Also, the fact that you said it would take the weight off your shoulders means you won't try as hard? That will just make your knowledge for the uni weaker and possibly get harder to achieve a 1st, 2:1, etc.