Good questions:
1) Jacketed bullets for 38 special tend to be light. Traditionally this is because 38 special pressures are low and there is some danger of heavier bullets being lodged in the barrel. I don't know how much of a problem that is today, but 110 to 125 grain bullets made for self defense are probably the best options.
2) Reloads and light loads are available commercially. These are typically in 140 to 160 grain unjacketed lead bullets. These produce less recoil and blast, and therefore encourage practice. They are typically less expensive. However, some makers of some models of revolvers, like the new very light Smith and Wesson revolvers explicitly warn that only jacketed bullets should be used. Don't ask me why.
3) +P loads require guns that will handle the extra pressure. That usually means any gun that has been built within the past 50 years by a major manufacturer. The extra pressure isn't that much higher than the standard pressures. +P cartridges will usually fire bullets a bit faster than standard cartridges. I'm guessing 50 to 100 feet per second in a 38 special snub nose.
4) Your hand size and stature have little to do with your recoil tolerance. The guns really don't recoil that much if you look at it objectively. However, it can take a while to get used to the idea of something going "bang" at an arm's length. Learning to shoot involves developing the understanding and belief that the gun won't hurt you when you fire it. In my case, for example, recoil isn't much of an issue, but noise is. It took quite a while to get used to the noise.
5) Not all ammo is equal. There are qualitative differences between them. For example, one brand may have a lot of flash when the shot goes off. Others won't flash very much. This can affect your shooting as it may be disturbing to see a lick of flame shoot out the gap between the cylinder and the barrel.
6) Fortunately much of the ammo for 38 special today is developed with the snub nose revolver in mind. Check out the less expensive jacketed bullets made by Blaser, PMC, Federal American Eagle, and Winchester white box, and I don't think you can go wrong.