I'll go into more detail of the various tools in dedicated posts. Here's an overview:
If you're only working on very small trees, shrubs, etc., it may be possible to get by with only hand pruners, provided you do have hands and the tree hasn't been growing long without needing pruning.
But you're probably gonna need more. In order, these are the tools I use the most.
First, alcohol. What fun is pruning, and where would the great stories come from without alcohol? Actually, rubbing alcohol is what I use to disinfect my tools between trees and between cuts if necessary. Mostly what you read about is a bleach solution, which is cumbersome and corrodes the blades. I think alcohol is much more practical. They have it in little spray bottles, which you can carry in a belt pouch, and it's faster than wiping. I can only imagine that alcohol is a better disinfectant than bleach or Lysol. It is, of course, what they use in hospitals, which have higher standards of sterility.
Then, you should really wear gloves. I've done plenty of pruning without, but there's no good reason.
And shoes. You want good, stiff-soled shoes for this work. Sneakers don't really cut the tough stuff and don't grip ladders that well. Steel toes are a good idea, too.
Wearing a helmet is a great idea. A branch could fall on you or you can fall off a ladder or roof, or out of a tree. I like using a bike helmet, which ventilated, fits snugly, and is comfy.
Safety glasses. Ok, I'm guilty of not using these much of the time, but there's little excuse except for misplacing them. You should have clear ones and sunglass ones.
On to the tools:
1. Hand pruners. There's are an absolute must. Get a good pair, or at least a mid-range pair, to keep from damaging your trees. Recommended brands include Bahco, ARS, Felco and Corona, but there are tons of brands that work well. I also frequently use my Japanese bonsai concave pruners quite a bit. Love those.
2. Long-reach lopper/pole loppers. I use pole pruners more often than short loppers. I have several different styles depending on the need. I have a Corona 6' model with an articulating head that lasts me cut up to 1-1/2". It's great, but the head sticks shut all the time, making it a bit frustrating. I can't figure out how to keep it from sticking. Oiling doesn't do the trick. I have a Fiskars ropeless pole pruners that goes to about 12', with an articulating/tilting head. It works great and is very user-friendly, but they become troublesome in a very short time, just a couple hours of use. I've returned two of them for a refund and then bought new ones. They're not terribly expensive, but work very well up until the time they don't. I have longer, standard pole pruners, but don't like using them as much.
3. Reciprocating saw. I stray from the crowd here. People tend to use either hand pruning saws (a bit slow) or a chain saw (cumbersome and rough), or a pole saw (too long for close work). I have a couple I use. One is two-handed, and cuts fast, and the other is single-handed, which works great if you need a free hand to stabilize yourself or a branch you're cutting. A reciprocating saw can also do the work of loppers, in about the same amount of time, and especially useful if you need to cut anything over about 1-1/4" thick, and they're much better with dead wood. I use corded models, but cordless ones are great to, as long as you don't run out of juice in the middle of something.
4. Extended pruners. I have a Stihl model that's about 7' long, which is like a hand pruner on a lightweight pole. This works much better on anything under 3/4" thick than a pole pruner/lopper. I actually use this tool almost as much as my handpruners. Love it.
5. Loppers. Short loppers are good at pruning branches up to 1-1/2" thick. And then it becomes a struggle for most people. There are some that go up to 2-1/2", but at that size you're probably better off with a reciprocating saw. I have various types and sizes depending on the application. Avoid buying discount brands. They'll be a hassle and fall apart almost right away.
6. Ladders. I have a 10' orchard ladder that's a dream to use, much better and safer to use than a stepladder. If I smarten up, I'll get a standing platform to save my feet. It's not tall enough for a lot of things, so extension ladders are needed sometimes. With those, however, you should have some rope to tie them off if at all precarious. Standing on a 10' orchard ladder, up to the 7' rung, I can reach up to about 21' easily with my extended pruners. If you're cutting a tree about 24' high, this is perfect. Orchard ladders come taller, which is a good idea much of the time. I have carried my orchard ladder on top of my car, with padding underneath and ratcheting straps to hold it to the roof. This worked surprisingly well. But I really should have a truck.
7. Pole saw. I don't like using a pole saw very much for various reasons, unless there's no other way. You usually get a saw that comes with pole loppers, but the blade are really too short. The really good ones are very expensive, and I haven't gone that way yet. These can lead to disastrous consequences if you don't think through what you're doing.
8. Binoculars. What?! These are very useful for evaluating what to cut. Dead wood can be spotted from a distance, and if you need to use a pole saw, you might need someone looking at your positioning from a distance as you start cutting.
Other things you might want:
Took bag/holster. Once in a while I keep hand pruners in my back pocket, but regret not having my bag or holster. You might want a bag large enough to hold alcohol, protein bar, or good luck charm.
Buddy. It's gross to have someone close for various reasons. But try to train them not to say what most people say, "there's not gonna be anything left of that tree when you're done, yuk yuk".
Hot tea. Winter pruning can get cold, and hot tea is really comforting.
This list could go on and on, but I'll stop there.