Somethings are better learned from dry firing than from live fire, so if you do choose a rimfire, get a good one, get some snap caps so you don't damage the edges of the chambers, and begin your practice at home. Remember that when the hammer falls, the bullet will hit what the front sight covers if it were live fire, and you will clearly see what the sight covers when the hammer falls when your sight picture is not disturbed by the violence of live fire; even with a rimfire. Practice loading and unloading the gun, you'll have to load and unload far more often then you'll shoot it. If you choose a centerfire gun, you don't need snap caps to dry fire, but snap caps or some easily identifiable dummy rounds are useful for loading unloading drills, or to practice clearing stoppages if you choose an auto pistol over a revolver. If you want to practice drawing the gun from a holster, snap caps or dummy rounds are useful here to. The draw should be smooth and fluid, so start slow until you get the steps down, and speed will come with practice. Again, the gun will be drawn and returned to the holster more than its fired.
Lots of guys have presented the positive aspects of choosing a rimfire pistol as a first gun, but lets for a moment consider the negatives.
The report of a Hi Speed .22 LR from a typical 4.5"-6" barrel is louder and sharper than the deeper flatter bang of a .38 squib load. Yes you can get standard velocity .22 LR ammo, but when you're at Canadian Tire and suddenly remember that you need a brick of .22s, guess what you'll get.
While everyone has pointed out the low cost of rimfire shooting, using primer propelled wax or rubber bullets in a CF revolver costs no more. You might want to dedicate some brass to this chore and drill out the flash holes so the primers don't back out. Recoil is almost nonexistent with these rounds, but they are a bit smokey. A .38 or a .44 pushed into a cake of paraffin and fired with a primer will penetrate a cardboard box at 20' so this ammo is not benign and should not be used carelessly.
The bigger that the holes are in your target, the better your shooting will look. Lets say you shoot a 4" group at 10 yards. If the holes are from a .45 the group looks quite good (although its not) and you might be tempted to carry the target around and brag a little. But shoot a 4" group with a .22, and you'll be tempted to squirrel the target away where nobody can see it.
Next there's what I call centerfire fear. This happens when a shooter who is trained on a rimfire rifle or pistol moves up to a centerfire gun. There is a sense of foreboding which he must fight his way through, although this can usually be put aside quickly with the firing of a few rounds, but it does present a real barrier for some. For that reason I would prefer to begin a new shooter on both rimfire and centerfire guns at the same time and if that's not possible then begin with a centerfire. I started my grandson on a light loaded .30/06, and he's turned into a competent and confident field shot.
The last one only applies if you shoot outdoors in the cold. Rimfire ammo doesn't shoot well in the cold, and you'll freeze your fingers attempting to load the gun. Centerfire ammo is large enough to handle with thin gloves on, and the cylinders and magazines of centerfire guns are typically easier to load.