Get a basic Airweight like a 637 (exposed hammer like your old Model 36), 638 (shrouded hammer, but can still be cocked) or 642 (enclosed hammer, double action only). They carry in a pocket holster so easily, you will not even notice it is there. For pocket carry, which is what you will want so you can have it all the time, the 637 is a little trickier to present from the pocket unless you learn the "Massad Ayoob method," which is to put you thumb on the back of the hammer using your thumb to form your own human hammer shroud. Works like a charm, but you have to remember to do it. In any event, I do not see the point of the "Gunsmoke special" or whatever it is called. J frame actions are heavy, yes, but ignition reliability is FAR more important. The short 629 you mention is a belt holster only proposition, and that will tempt you to leave it home when you are not dressed for it, and that requires a fully functioning crystal ball so you will know on what day you will be "in the wrong place at the wrong time." I find the steel J frames too heavy for efficient pocket carry and, as I said about the 629, you will need a belt holster, which will mean a covering garment, which will mean you really won't have it all the time.
So, if you really want to be armed (your revolver is with you if you are wearing your pants, both in your home and out), then get an Airweight J frame, some FBI loads or the Speer Gold Dot Short barrel ammo and a speed loader and you are set. As to pocket holsters, there are three really good ones that I can recommend from personal use. There are others, but these I can speak to from personal experience. Bob Mika, former LAPD, makes a great one and he is a personable guy who will take care to make a good holster for you. The Safariland pocket holster is also very good. Remember that you will have to order it "side specific," and that is its one downfall. More on that in the next paragraph. Finally, there are two "available now" options from Elite Survival Systems. The first is their pocket holster. The second is their belt clip holster, which, with the belt clip removed, makes a dandy pocket holster. Nice straight cut across the bottom to distribute the weight of the firearm in the pocket. Please do not get Uncle Mike's pocket holster. The one I had "collapsed" after only a couple of weeks and the straight bottom folded over resulting in the revolver not riding straight up in the pocket, which meant a visible and unnatural and noticeable bulge in the pocket.
As to pocket holsters, the disadvantage of having to order "side specific" is that some people like to wear in strong side pocket if that is the only firearm carried, but switch to weak side if the pocket pistol becomes a back-up to a full size pistol is worn strong side in either an OWB or IWB holster.