I decided that fake plants would probably work better at the new apartment, since I can't imagine the landscapers would appreciate me digging up their plants to replace the ones my birds eat... I bought a fake vine and millet stalk on sale for $10 from Hobby Lobby to see how the birds would react; they didn't try to eat any, so I figured it was safe to get more.
A few days ago, the Betty Griffin House thrift store had fake plants 50% off, so I bought a bunch for $10. I had to pull several out of the foam, and all of them needed a decent wash, but it was worth it. If I got this volume of plants from another store, it probably would have cost 5 to 10 times more.
My mom also found a sturdy hexagonal birdcage that's around 3 feet in diameter for $20 at another thrift store a couple months ago. I'm working on sanding and painting it, and hopefully bring it with me, as well.