I go all the time and I am constantly improving......adding things I need and getting rid of the things I don't use. Here's what I do:
I use a nylon tool bag (light but strong) with both handles and a shoulder strap. It has lots of pockets on both the inside and the outside. You can strap it over your shoulder when it gets heavy. I have used both the wagon/dolly with wheels and the bucket in the past . The wagon is too bulky for tight spaces and the lot I use has large rocks/pebbles as a base. It also has debris and parts from the cars scattered around so it does not want to roll well. It just tends to get hung up a lot. The bucket is just plain too heavy when filled plus the tools are at the bottom so when you fill it with parts they are not convenient to get to.
OK tools: A socket set with both metric and standard sizes is a must. Also you need the same sizes in a box head and open end wrench set. It sounds crazy but I have run across instances where only one of those will work. Also many different sizes and shapes of screw drivers are good. Very short (for tight places) as well as long for prying. I use a screw driver with replaceable heads so i don't have to carry multiple shafts around. You need some pliers and vice grips also some cutting tool like shears for wires and such. I take work gloves and protective eye wear for when you need to get in a tight space. I also take a pad of paper and pen to write down info when taking something a part also what row the vehicle is in in case I need to go back. Still no matter how well prepared you are you may still need to leave and go back with another tool as you simply can't carry everything with you.
Of course if you are getting a bigger part then you will need a wagon or dolly of some sort.
I don't mean to be saying my way is the right way, this is just what works well for me. As I said previously I am constantly changing my routine as I go two to four times a month. Good luck on your junk yarding, it's good fun.
