To the OP, I would suggest that if you are going to start with squirrels and work your way to deer, then sort of hunt the squirrels like people would hunt deer. I realize that you aren't totally familiar with that, so I will throw out a few examples.
Work on your quiet, still, moving slowly game. Squirrels don't spook like deer, except at really close distances. Do nothing quickly. This will also help you get your gear sorted out as to what makes noise and what is quieter. For example, I learned early on that I chose a wrong sling for my rifle because it made metal on metal clinking noise. That disappeared after the 2nd hunt, LOL.
I don't know how accurate your 10/22 is at any given distance, but work on your precision shooting. If you are shooting through heart/lung/thorax to make your kills, then work on brain shots. This is important and I cannot stress this enough, LEARN THE ANATOMY of the critters you hunt. A lot of basic hunting teaches a lot of really oversimplified broadside shooting considerations which are often the easiest to convey with 2D anatomical images, but animals are 3D, not 2D and so that opens up a lot of addition angles (which will come with more experience). My point here is that it can be very helpful to your success that when you fire your shot, you anticipate based on the aim and trajectory that your round will hit this, this, and this inside the body that you want to hit in order to speed death. Where the 3D aspect comes in is that sometimes you want to hit this and this, but not THAT and so you hold off on your shot until your aim and trajectory will carry the bullet through the structures you want to hit.
Skinning out your game and examining the damage done by your projectile will tell you a lot about your shooting and bullet performance and help get you familiar with anatomy. While most mammalian anatomy is very similar from a general perspective, organs are often larger or smaller (relative), more concentrated or spread out, depending on the critter. Using a simplified example, take brains. Let's say you decide you want to make brain shots for some reason. The relative sizes of the brains will differ between many species and how the brains are situated in the skull may differ. It may be safe to make most "head shots" on a squirrel and still get a kill from a .22, but you really want to be making brain shots to be sure that the bullet actually does brain damage to put down the animal. You don't want to non-lethally shoot the critter through the teeth (which would be a "head shot").
If you learn 2D deer anatomy and where to shoot a broadside deer based on 2D images and are presented with a strongly quartering toward shot and you use the same placement, you may end up with a bullet in the abdomen and all the lovely gut juices getting all over the meat you want to harvest.
Here I will make a comment based on my own experience with a buddy. If you have really been into self defense sort of shooting, strive to NOT make COM shots and centerpunch your animals. Maybe you hit the liver on your deer and it runs several hundred yards, bleeding out, but not very quickly. The liver isn't necessary a terrible shot (some archers love it), but your tracking game may need to be good and as a newbie, it won't be. A fireman buddy of mine makes a lot of money each season being on call on his days off, with his well trained dog, helping hunters find their lost deer because their tracking game isn't up to the task. Of course, tracking is a whole other skill set to learn along the way, but it is better to start with short tracks and quick kills than long tracks and slow kills.
So particularly at the early stages of learning, you want to also learn how to NOT pull the trigger. "Buck fever" (oddly enough, male squirrels are also called "bucks") has ruined many a hunt and a lot of first time hunts. I would even suggest for your first hunt that you watch the squirrels behaviors and learn how they move about where you are hunting. Maybe take your rifle, unloaded, and practice dry firing (or just pressing the trigger slowly and smoothly on an uncocked rifle because this is a .22) and NOT upsetting your sight picture. It is really hard not to get excited and adrenaline is NOT your friend when it comes to steady shots. So basically, you are doing stress inoculation. It only took me a few years to get to the point where I am not fighting adrenaline, LOL. Some people never get over it, but they learn to work through it.
For the first squirrels you see when you are first locked and loaded, track the squirrels (assuming safe directions) with your rifle, but don't fire it. Work on being calm and choosing the shot you need to make for a clean kill. Very little about squirrel or deer hunting should be a life or death experience for you. You don't have to shoot! That is one of the hardest things newbies have issues with. Those first few opportunities come up to shoot and you would think they were never going to have another opportunity again and that their whole and only hunting experience was going to be at that moment and they don't want to miss it. Very few people die after their first hunting experience with opportunities to hunt again. Don't stress if you don't pull the trigger. Not pulling the trigger is sometimes the best shot you can make at the moment.
Congrats on getting a mentor to take you hunting. Listen to what s/he says. Do exactly what they tell you to do, but start learning your anatomy now.
