The 638 offers both SA & DA and was my first, and still most-carried, gun. Others will suggest the 642 or 442 (DAO) and that would also be a fine choice. The factory triggers on Smiths are a bit stiff, but I had my trigger smoothed out by the gunsmith at a LGS and it is great. You may want to consider some trigger work after you feel the weight of the trigger pull. A gunsmith may also be able to smooth up the release latch for you. Since recoil can be an issue for you, the lighter (non-steel) guns will provide more felt recoil. You could practice (and you do need to practice to get used to the j-frame!) with light wad cutter loads most of the time and carry them if you feel ok with them, or use a standard pressure .38 JHP load (not +p). Lastly, you will want a decent pocket holster. Lots of guys use and like the Desantis Nemisis. That was my first pocket holster, but I found that it would not stay in the pocket very well. Check out the holsters by Robert Mika. They are very well-made and about the same price as the Nemisis. I now have a couple of them and they are great.
Welcome to the forum. You'll get lots of great advice here.