Hey c.fly,
I suppose you have already made your decision, but if you are asking my opinion I would recommend Union Court. Otherwise, you have to look for an apartment alone and also to communicate with the owner. I prefer accommodation managed by the university, as they would take care of any problems I may have. Moreover, I heard Union Court is a quite good choice in good location(near the bus stop and the train station). You also have your own bathroom and your own room and you share the kitchen.
Spairos,
This will be my first time in Warwick. I was an undergraduate student in Greece. I applied for accommodation at the end of June.