I'll go in a slightly different direction then most and I'll explain why. I like have multiples of the same firearm in different calibers or as close to each other as possible. I even go as far as having replica pellet/bb guns of those same firearms. I like to warm-up or practice, usually with a 22 version and then move on to one of the others. The pellet guns make for an impromptu for the back yard or basement/garage during a snowstorm. On one hand in your situation, you want a home defense revolver and by far, a DA model would be better for that role. On the other, your also stating that you've become comfortable and proficient enough with your 22 SA to want to move on to a centerfire. The DA's and SA's are two different handguns in the way they handle, ergonomics, operate and in the way they recoil.
If I were you, I'd probably would stay with a SA more then likely and as others mentioned in 357 and from the same parent company if possible as your .22. I reload and use two basic recipes for 357's. One for me and one which has less recoil for someone I may be teaching to start with instead of using 38 specials. One of the benefits of reloading. I say stay with the SA for now and at some later point develop a line for DA's if you wish.
Here's a few with overlapping calibers in both DA and SA. Left side down is a 629, 686 and a 617 and the right is a pair of Vaqueros and a single 6 convertible. Some firearms I have two of as I use both hands as in these 1911's and so on. There are some I use exclusively right handed though I'm lefty like a PPK/s because of the de-cocker, most I use lefty. It takes practice to get used to using two.
Because I use round-butt grips, the "recoil" will act the same on the DA's as the SA's, in other words they will have a roll-up movement as opposed to a more straight back push as in my 29 or 27 with their original square butt grips.
As for a sampling of an airgun replica, here's a shot I made for an airgun forum. The bottom on is the airgun. For the Smiths I have a Uramax 586 but no photo.
JETA: Forgot to mention. Most, if not all SA with the traditional sights will have an extra tall front sight. They are made that way so that if you wish, you can adjust them down for your own vision aspects. On the bottom photo, you'll see the two Vaqueros have been adjusted so. On most forearms I use a 6 o'clock hold. On SA's I like a POA, POI so all my "modern" SA's are slowly filed down to do so. For the faint of heart, my Colts are the same as when they were made.