I love SA revolvers, LOVE them! But for practicality, Double Action is the way to go. Unless you train a lot, and I mean 1000's of rounds, and use "powered-down" loads, a DA is much faster than a SA. DA's have the swing open cylinder which makes reloading much faster, especially when practiced with a good Speed-Loader. SA's are typically stronger and can take much more punishment (hot loads) than a DA.
I bought a used Model 29 (.44 Mag) and I took it back as the frame had been rattled and the cylinder knocked out of time, which was so slight, you couldn't tell until you went to shoot it. Had the same thing with a Taurus. Guys will try to run super hot loads through these things and they just can't handle it, so they dump them at the pawn and gun shops. In the mid 90's, if you bought a .44 mag, you had to assume that somebody ran a 300 Grain "Elk Load" through it. I was fortunate that when I went back to these places, they said "no problem".
A good SA revolver (like the Blackhawk/Super Blackhawk) will take just about whatever you can come up with, and be used as a hammer to drive tent stakes at night. And that's not to say there aren't "bomb proof" DA's out there, but they're designed for hunting and those hot loads. And they'll cost you. They're not something you would have as EDC. And again, even though "bomb proof", will fold long before a good SA.
I guess the biggest question is; What do you plan to use it for? Concealed carry? Camping or hiking? SHTF? Each choice has its application. Can you use a SA for self defense? Absolutely, but it has "Speed Limitations" and you better make those first six count because there is no such thing as a "tactical reload" with one. It one out, one in. 12 distinct motions to get your gun back in full battery.
If you are planning on working your way up to a .357, just go buy one and shoot .38 Specials until you're proficient with the revolver. Depending on what you're using it for, I would highly recommend the Ruger GP-100. It's a fine looking gun and tough as nails. If you're looking for a carry gun, Smith, Ruger and others make fine snubbies that will easily slide into the pocket.
I took my mom shopping and picked her up a S&W Bodyguard 38 (+P rated) for less than $500 at Cabelas. It is DA Only (hammerless) and comes with a built in laser. Nice, lightweight and with Hornady Critical Defense, you're good to go.
Ruger has the LCR in .357, but it seems a little much for that EXTREMELY light weight gun. They also have the SP101 Series, which I had purchased as a back-up gun when they first came out (a fine shooter but was a little heavy on the trigger). If you head the SP direction, just keep on going and pay a little more for the GP-100.