Aquaponics
Get proper training
Do a course before you spend a cent.
I learned the hard way that reading forums is no substitute for being taught the fundamentals: the nitrogen cycle, system cycling, fish health and water chemistry. Get those wrong and you kill your fish, your plants, or both.
I did Murray Hallam's aquaponics course and I recommend it. He is based here in Queensland, so the climate and the practical side of what he teaches map directly onto what you will be dealing with in a backyard like mine. Aquaponics.net.au is where you book the course, and he sells a lot of aquaponics gear there too if you want purpose-built kit rather than piecing everything together yourself.
A few more shots from Murray's farm: media beds, raft beds, and the plumbing that ties the greenhouse together.
Do the training, then come back and use the sourcing tips to build it on a budget.