Forget the .38 Special or .357 Magnum, or any other center-fire for that matter. The cost of ammunition will limit his ability to practice with it.
Get a .22 revolver, preferably double-action. With the double-action, you can either thumb back the hammer to fire it, or pull the trigger and it will cam back the hammer and fire it.
With a double-action revolver, the cylinder swings out to the left and the empty shells or loaded cartridges are ejected all at once.
A single-action revolver is not a bad choice, per se, but it takes longer to load and unload. You have to turn the cylinder and punch out each empty, or load each cartridge, one at a time.
I would suggest a double-action revolver of high quality. Spend the extra money and get him a Smith & Wesson or Ruger SP-101 in .22 caliber.
I suggest a 6-inch barrel. A 4-inch can be good but requires a little extra work to become good with it.
I have a Smith & Wesson Model 17 revolver (blued) with a 6-inch barrel. I also have a Ruger Mark 1 bull barreled semi-auto, a Charter Arms Pathfinder revolver with 3-inch barrel, an Iver Johnson TP22 semi-auto pocket gun and a Stoeger Luger.
Out of all of these, I'd suggest the Smith & Wesson as a first gun.
The revolver MUST have adjustable sights, not fixed sights. This way, he can move the sights to where the bullet strikes, at any reasonable range.
Aside from the lower cost of ammunition, the .22 rimfire has other advantages to it:
1. It may be used at any indoor range. Some ranges limit which cartridges may be used, because of their bullet trap. High-penetrating rounds like the 9mm, .357 Magnum, .38 Super and .44 Magnum may not be allowed, for example.
The .22 is always welcome at any reputable range.
2. The recoil is low or negligible. If he starts with a .357 Magnum, he'll undoubtedly want to try .357 cartridges in it. Yes, I know that the .357 Magnum can easily shoot any .38 Special cartridge. However, that temptation to shoot the .357 with full-power loads will be there. This is almost guaranteed to give him a bad flinch --- and may sour him on pistol shooting altogether.
Yes, I know that other 16-year-olds handle the .357 just fine, but we're talking about a kid that likely has limited experience with a handgun, if any experience at all.
3. He will never outgrow a good .22 revolver. They are always useful, whatever your age. A man may start his life with the big Magnums, but almost invariably he'll buy a .22 handgun because of its versatility and usefulness.
4. He can shoot ammunition in it that is very reduced, such as the .22 Short or .22 CB cap. This is good ammo for pests at close range, or just for plinking. If he wants to shoot very weak loads in the .38 or .357 Magnum, he'll have to make them himself.
5. The .22 will allow him plenty of practice, because of its low-cost ammo. He'll have plenty of opportunity to develop good shooting and safety habits. The absolute worst thing you can do is start someone with a Magnum with Magnum loads. They will invariably develop a flinch and bad habits, such as closing their eyes just before they pull the trigger.
Each and every shot should come as something of a surrprise, an expected surprise if you will. The .22 will cultivate good habits without the distractions of noise, recoil and blast.
I should add a note about the .22 rifle or handgun: more than any other firearm, it is very particular about its likes and dislikes. When you get a .22, you should buy a box of every kind of ammo you can get your hands on: Winchester, Remington, Federal, CCI, Wolf, etc. And don't overlook the hyper-velocity loads and hollow-points too.
Then, buy at least three REAL paper targets (not just a tin can) for each box of shells you buy.
If you can, use a benchrest and rest your hands --- but no part of the gun --- on a pistol stand or even a tightly rolled blanket or sleeping bag. Fire each brand single-action, by cocking the hammer first then squeeeeeezing the trigger at the target.
Write on each target exactly what brand and type of cartridge you used.
When it's all over, compare the targets. You'll be amazed at how your revolver prefers one brand over another, and perhaps even one type over another (hypervelocity, hollowpoint, standard velocity, high velocity, etc.) among the same maker.
It's tedious, I know, but in the end you'll have the most accurate load you can get --- and you'll have fewer misses.
Too many people buy the cheapest brand they can get. Sometimes it's accurate, often it's not. Find what that revolver likes and stick with it.
And when a new manufacturer or type comes along, try that too.
He may pooh-pooh the idea of "just a .22" now, but he'll thank you later for it. Many kids today (of all ages, unfortunately) want a "big ol' Magnum" so they can be impressed with its power and recoil. Marksmanship counts more than power.
Just starting with a handgun is NOT the time to use a Magnum or even a .38 Special, for the reasons I've stated above.
Later, he can move on to a .38 or .357 Magnum --- an excellent move by the way. Then, he'll have a good centerfire revolver AND a good .22 revolver in his battery.
Go with the .22 rimfire. It's the best for beginners.