I'm also a bit late, but I thought I'd throw in my two cents.
For small errands have you considered a cargo net? They are relatively inexpensive, but far more useful and convenient than bungee cords, I've had good experience with each of these for example: 1)
http://amzn.to/OiWmM0 , 2)
http://amzn.to/MmsThKI'm currently using the latter and I think I paid a little over $4 for it from REI on sale. Cargo nets combined with a rack are surprisingly versatile, they are good for quickly securing a backpack to a rack, and can also hold down bags of groceries easily if you have the right technique. I think I've managed to hold two large reusable grocery bags plus a large bag of ice in the past.
I do own a pair of panniers (
http://amzn.to/OiYEej), but only ever needed to use one. I bought them as a pair on sale from REI, ended up selling the extra one and accidently made a profit that paid for the cost of the panniers (longish story). I find this my to go thing for most stuff, but the cargo net fills in when I don't want to carry around the pannier.
As for attaching boxes, crates to the rack, I've done this in the past using things ranging from bungee cords, to zip ties, and now screws. In fact I have to attach something to my rack soon, I will try and post pictures if it works out.