What can I add? Well, I can't keep quiet -- ever -- so I'm going to chime in here, late as usual.
Besides having permission, I always want to make sure the neighbors aren't going to get ticked off at my being there in their territory. Even if we do everything by the book, there are still some people who are going to hassle us. So if/when anybody hassles me, I politely leave. I might go back if I have a good feeling about the potential there, but I'll go back when I figure people are still asleep -- very early in the morning.
Then I want to make sure I wear sturdy shoes with tough soles, in case I walk through broken glass or rusty metal -- which is often typical in out-of-the-way places.
I have gloves and usually carry an extra pair in my pack
I take a small backpack that holds my small stuff, and I usually take it off and hang it somewhere so that it doesn't confine my movements and so that I can see it when I move on. Putting green or brown packbacks on the ground is not a good idea! In fact, get a brightly colored backpack and you will have a better chance of finding it if you do put it on the ground. Wearing a red backpack will also make you easy to spot -- which can be good or bad, depending.
Besides the required water, wet wipes, first aid kit, gps & compass, I take a pocket knife, and some survival gear -- very lightweight but gives me a greater feeling of security. Never had to use the stuff for myself, but have used it for some strangers through the years. And don't forget the camera and the notepad and pen. You'll be surprised how often you'll want to jot down notes about the place or about what you found and how. A notebook is a very handy thing -- but useless without a pen or pencil. Don't forget extra batteries and a long-handle digging tool (which makes a good weapon). I don't carry a gun anymore, but used to when I was young and more attractive. Now I can scare off most people with my demeanor.

It's known as having a certain attitude -- like "don't mess with me buddy because you'll be sorry." (I learned this attitude when attending a solo woman's hiking seminar that was offered at a national park many years ago.)
Most of all, be aware of your surroundings and look up and around frequently. I've had many "sneak attacks" by people and animals when I was concentrating on my digging instead of my surroundings -- fortunately they turned out to be friendly. It is frequently hard to pay attention to the digging and to the surroundings simultaneously, so I will often detect with one ear clear of the headphones.
As a woman who goes alone quite often, I have to say that most times everything goes without trouble. On rare occasions, somebody is watching me a little too closely or walks too close to me. In those situations, retreat is the smartest move, IMO. If I can't retreat fast enough, I will not take my eyes off the person and I keep my long-handle digging tool in my baseball bat grip.