For revolvers where you might be shooting a variety of bullet weights and power levels it does help. A fixed sight revolver is going to be limited to one or two bullet weights that produce the same muzzle rise by the time the bullet leaves the muzzle so they hit at the same point as your sights show. The terms for these if you have not seem them are Point Of Aim (POA) and Point Of Impact (POI).
For example the .38Spl model 10 S&W has fixed sights and it is sighted in for 158gn bullets (any style as long as they are 158gn is fine) shot with a full power load for .38Spl. Shooting 125gn bullets means the bullet will be faster in the barrel so it leaves earllier and does not produce as much of a muzzle rise from the recoil. So the lighter and faster bullets have a lower POI than the sight's POA.
And that is where adjustable sights on a revolver come in handy. They allow you to use whatever ammo you can find and be adjusted easily to suit the new POI of that ammo from your gun.
There is one notable exception to all this. With the fixed sight gun a round which duplicates the muzzle rise of the 158gn regular load will still print at the same POI. This happens to be the classic 148gn target wadcutter bullet. The most classic of these are the hollow back wadcutter. But the double ended "beer barrel" wadcutter also produces the same results. These use a very light charge and are good for even the most recoil shy person. They barely make more kick than a .22.
If you go for a .357Mag revolver you can shoot either .38Spl or .357Mag from the same gun with no changes needed. But you can't shoot .357Mag from a .38Spl gun. For that reason many/most opt for a .357Mag revolver. And for THIS case I strongly urge getting a gun with adjustable sights. You WILL need to adjust quite radically between shooting any magnum rounds and any .38Spl.
For example, I often used to play a little shooting range game I called "Revolver Roulette". The idea was based on the cartridge boxes having neat rows of 5 rounds but my revolver held 6. So what better to keep things even and fill the extra hole than a round of .357mag....

I'd give it a spin and stop the cylinder and close it without looking. BOY! Does THIS tell you quickly if you have a flinch!

But back to the sights issue. With the gun set up to shoot the 125gn .38Spl the magnum round came out so much faster that at 12 yards it had a POI which was about 3.5 inches lower than the rest of the group. THAT is how much it matters.
Most of us do shoot a much higher percentage of .38Spl from our .357Mag guns. I suspect you will too. But even so while I love my K frame S&W's I also know that they don't take nicely to a diet of a lot of .357Mag. A few now and then are OK and especially if the rounds use the heavier 158gn bullets to hold the speed in check. But if you'll shoot more than a few now and then I'd suggest the L frame 686 S&W. Or if you're a fan of blued guns then get a 586. If you want to shoot almost nothing BUT .357Mag then the N frame Model 27 or 28 Highway Patrolman might be a better option. But in that case you may want to just pony up for a Model 29 .44Mag and be done with it...
There's a somewhat steady flow of ex-prohib K frame .38's showing up. These have had a new barrel sleeve installed and a button added to the front of the barrel to extend them to 4.2" or a hair more. This has taken some very nice guns out of the prohib pool and allowed us new shooters to join in the fun of shorter barrel revolvers. I've managed to score two such guns and they are staying with me until I'm too blind and decrepit to shoot any longer. Like I say, I REALLY like the compact K frame guns. Most others just buy the L frame 686 and call it a day.
If you prefer blue over stainless look around and get to know the models a little more. It's all good and you don't need to buy one tomorrow. Although I understand how SOS (Shiney Object Syndrome) can drive any of us....