Talking about "number" profiles is a waste of time.

For any calibre your minimum thickness will be calibre plus 90 thou each side. Tapering from there back to the action dia which is fairly common on a Remington 700.

So, for your 358, your minimum dia at the muzzle is 540 which is just a hair over Remington Mountain Rifle profile. FWIW the original Rem600 barrels were 18.5in and .610 at the muzzle. These came in a 350 Rem Mag.

Standard Remington Sporter would be nice, but IMHO the Remington Magnum profile will be more suitable at about .650 for your chosen length. This profile chosen as your stock may not be as light as some and the slightly heavier barrel will give you a better chance of having a rifle that balances nicely. Read up on rifle balance, but the short version is about 4 inches from the trigger is where a stalking rifle should balance.