I'm all for making your bike work for you. Whether you use a front or rear rack/basket you'll probably need to tie your stuff down at some point. I see a good number of folks using bungee cords to do this. I think this not a great idea for a couple of reasons. One- Bungees store up an explosive amount of energy when you tension them. Two- They have sharp metal hooks on the end. When the bungee lets go it sends that hook flying- into spokes, eyeballs, freewheels/cassettes, around hubs. The motivation for this post was a Hub Hall-of-Famer who came in last week after getting a bungee all wrapped up in his spokes, and had a slow motion crash situation. I'm not a fan in general, but especially not on rear racks, because you can't keep any eye on that deadly bungee.
What else are you suppose to use to tie stuff down, then? I have two better options. One costs a little bit of money, the other is basically free. Let's talk the money option first.
Toe straps. Those little guys you use on your sweet old school toe clips (or cages, if you must). They're made of nylon webbing, or leather, with a metal clasp at one end. The clasp has some little teeth that help hold the strap in place after you've cinched it down.
They hold nice 'n tight, without being elastic/explosive. The down side to using these guys is that they're pretty short. They're really designed just to go around your foot and a pedal, which doesn't take much material. You can attach a couple of them together, but there is a limit to what you can hold down. Surly fixed that problem by making Junk Straps- extra long toe straps for carrying junk.
Toe straps cost $5-10 for a pair, and the Surly Junk Strap costs $8. Super useful and versatile. If you want something for cheap. Super cheap. And you like recycling/reusing, you should think about using a dead tube. They're stretchy without being snappy. You can cut them to be whatever length you need (within reason). You probably have one laying around, if you've ever fixed your own flat tire. If not, you can come to the shop and take as many as you'd like (within reason).
To use the tube, cut it so it's no longer a circle. I personally like to cut the valve out, for convenience. Wrap it around your cargo/rack and tie a knot or two. Piece of cake. You can then either untie that knot or just cut the tube to free your cargo. No crashing or losing eyeballs.