There have been some good suggestions.
Being that I started hunting with air rifles I would agree that shooting a .22 firearm is a bit easier, many times they are lighter and easier to be accurate with than most spring or nitro-piston air rifles. The reason I say .22 firearm is easier to be accurate with is that nitro and spring piston air rifles have what is referred to as "double recoil" due to the forward and return motion of the piston when fired. They require, typically, for the shooter to use the "artillery hold" (look it up if you aren't familiar with it) in order to achieve good accuracy. The one draw back with a .22 right now is getting ammo, while .22 pellets are readily available almost anywhere airguns are sold.
The Benjamin NPXL1100 is a nice break-barrel air rifle. However, the are heavy for a smaller person to carry around or shoulder in the field when hunting. The included scope is decent. The trigger is glitchy and needs work also. I did own one in the past and liked it, but I like my PCP air rifles better.
Benjamin also makes the Titan model which is a little smaller and lighter than the NPXL, but the pellet velocity is also lower (less powerful nitro-piston or spring piston).
Gamo's air rifles are typically lighter and they have allot of models for under $150 to $200, but most of those are spring piston models and the velocities they advertise are bogus because they get them by shooting their PBA ammo that is inaccurate past 10 to 15 yards. The scopes that are typically included are fixed objective and not very good (just my opinion). Also, one thing to keep in mind about spring-piston air rifles is that if you leave them cocked for extended periods of time the spring starts to compress, and this leads to a slow loss in pellet velocity over time.
Gamo does make an smaller sized air rifle called the Gamo Little Cat. It is a .177 caliber spring piston air rifle with a wood stock that has a length of pull sized for smaller arms. It had a loudness of Medium, with is about average. It will "pop" some, but not "Crack!" when fired. It is a break-barrel rifle that weighs about 5.5 pounds. You could probably expect velocities with lead pellets at around 600 to 650FPS, depending on the grain weight of the pellet.
As TaftHunter mentioned, check out Pyramydair.com before you go to purchase one. They have videos you can watch also too learn the differences in the various types of air rifles. Also in the specifications for each gun they let you know how loud you can expect the gun to be on a scale of 1 to 5.
If you have any other air gun questions I'd be glad to answer any you may have. I currently own a Crosman 2240 pistol (modified), a Benjamin Discovery in .22, (2) Benjamin Marauder Pistols (.22 cal (one is modified for my daughter to shoot it), Benjamin Marauder rifles in both .22 and .25, as well as a EunJin Sumatra 2500 Carbine in .25 cal. In the past I have owned the Benjamin Trail NPXL1100, Gamo Whisper in .22, Ruger Air Hawk, Ruger Black Hawk, Ruger Air Magnum, Crosman 1322 (I heavily modified it) and a Crosman 1377 (rebuilt and modified). I have also rebuilt and modified quite a few different air guns for friends and family too. I'm NOT posting that information to show off, it is just to let you know that I'm speaking from some experience with air guns.
One thing I thought I would mention since you mentioned taking your son hunting is that technically your son can't legally hunt squirrels, rabbits or other animals without a hunting license. He can go with you as a spectator without his airgun, but if a warden sees the both of you with guns (even airguns) he can ask to see both of your licenses. I know this because my 8 year old daughter goes with me on hunts without her airgun and we've been approached a few times. They've asked me if she's hunting and I tell them she is just watching and learning to hunt by watching me, that she is not shooting at any animals. I only mention this because some aren't aware of this and I wouldn't want anyone to get in trouble.
Whatever you decide to get have fun and shoot safe.
