In one regard it is a bit of a on brainer - get a .357, as you'll always have the option of shooting .38 special in standard or +P loads in it.
I also agree the extra weight will make it more pleasant to shoot, regardless of the loads you choose to shoot in it.
A major problem with snub nose .38s is that with standard pressure loads, they tend to have poor terminal performance. While many .38 special loads perform well in a 4" revolver, even the best standard pressure self defense loads when fired from a 2" pistol are not any better than the best .380 ACP loads fired from a 3.9" semi-auto. From that perspective, .38 +P loads are pretty much the minimum for 2" revolver use.
Personally, if I were set on a 1.85" to 2" revolver, I'd select an all steel 2" revolver in .357 Mag, something like the S&W 627. It's a pound heavier than an LCR, but IMHO much more controllable with .357 Mag or .38 +P loads. The extra weight helps in terms of making it much more shootable and with a decent belt an holster you won't mind the extra weight.
If you have your heart set on the LCR, consider the 3" barreled 5431. It's a .38 +P pistol that only weighs a pound, but it's a good compromise between weight, size and ballistic performance as a .38 +P load in a 3" barrel won't be far behind a .357 Mag in a 1.85" barrel, yet it will be less painful to shoot.