Ok the graduate jobs you need to get advice on. The priority is your degree, then your sell point is what youve told us, you had a bump, but you learned from it, went to uni and youve overcome it. If they are rejecting you then you just need to find the firms that wont use it as a stick to beat you with, the rest are irrelevant.
The LL thing is really you avoid agencies who milk credit checks or if its an agency with a house you must have then you offer it all in advance. One ood way is halls for first year , make your friends and move out with them. Private LL's tend to be much more flexible, but be careful about offering a years rent. make sure you wnat it and then get receipts etc.