Cage

I was thinking about getting a rabbit(yeah I know I think about getting a different animal every week but I really want a rabbit). And I plan on making it a house rabbit sorta it wont be loose with the cat but on a leash. So I don't really need a cage except when I'm not home. So I was wondering if I should build a c&c cage for it and how big it should be. Or if I could use my old guinea pig cage if it was just for night time.The cage is about 32" x 20" x 17" on the inside.Here's the picture of it. First the companies picture , then a picture I took(ignore the mess I had just moved the pigs out when I took that picture) . It's pretty big. Just big enough for a rabbit to sleep in a night. Does anyone think I should use it or make a costom cage? And if anyone has advice on how to get my parents to let me get a rabbit it's welcome. I have space and time and I can save up the 130 dollars about that I need. I plan to keep the cage in my huge closet with one of the doors open when im not home.Thanks for the help.