The decomposing matter, especially in large quantities, will attract large numbers of bugs attracted to decaying matter such as sow bug and pill bugs. The bugs will attract predators like wasps, but not to worry, you can find a high-quality wasp trap here .
Look after your containers. That you do not have to spend
You can purchase a bug hotel here http://www.amazon.com/inches-Insect-hibernation-Keeping-Shelter/dp/B00NM3MOEC to best encourage other insects and place the bug hotel near your roses for example.
Obviously, you will need a rabbit hutch, and there are rabbit hutch plans you can buy from here http://www.amazon.com/Rabbit-Production-Guides-homesteading-survival/dp/B00K7RDU2G if you are going to be completely organic and build your own.