Hi again, L!
The .38 special model 649 (-1 or -2) are 20 oz guns.
S&W lists their model 649-3 (or later) at 23 oz.
The .38 has a 2" barrel with the .357 Mag having a 2 1/8" barrel. S&W did make a limited run of 649-3's in .38 Special with a 1 7/8" barrel in 1997.
The 649 series will handle .38 +P ammo just fine. The recoil shouldn't be significantly different between the different variants.
For under $300, I'd be whipping out the Visa card in a flash!
Personal favorites for this gun are the W-W 125gr Silvertip JHP .38 Special +P and the Federal HydraShok 129gr JHP. I have yet to try the Speer Gold Dot or Remington Golden Saber however.
Below is a photo of a .38 Special Model 042 (Model 42) Airweight .38 versus the newer Model 649 in .357 Magnum. You can see the barrel differences between the 2 1/8" magnum and the 1 7/8" .38.
Note: In the photo above, you can see the 649's "J-Magnum" frame & cylinder are slightly longer than the .38 special version. This adds to the overall length of the gun slightly too. Your .38 special version, unless it's a 649-3, will have the shorter J-Frame & cylinder.