I've put hundreds of 125 gr .357s through a Model 65. No worries. The round
is stiff to shoot, generating a fair amount of recoil.
There is no functional design difference between the various classic S&W .357 K-Frames (13, 19, 65, 66) except for barrel contour and sights. They can all handle any commercially available .357 load. To reach the level of flame cutting or forcing cone damage you are worried about, you'd need to be shooting several thousand 125s through your revolver.
All three of the rounds under discussion are viable for use in your 65 and of proven lethality.
I recommend (and use) the .38 Special +P 158 gr LSWCHP (known as the "FBI Load").
Among the all time top performing .38 Special loads, this round has delivered the mail for decades. It offers a sweet spot blend of controllability, adequate penetration, reliable expansion, and combat accuracy
I use the same load in my HD .357 service revolvers because the heavier .357 frames tame +P .38 recoil to pussycat levels, enabling rapid and accurate followup shots. The bullet itself is one of the better anti-personnel designs ever offered.
Additionally, I don't want a lesser trained family member to have to deal with distracting noise, muzzle fireball, and recoil management problems generated by full-house .357 loads in the house.
Remington's version, travelling at ~890 fps, uses the softest lead (possibly enhancing deformation/expansion in flesh), but Federal and Winchester sell the same load. Buffalo Bore also makes a 1000 fps version with a good reputation.
http://www.buffalobore.com/index.php?l=product_detail&p=108
Hope this helps...