Since you are fairly new at this, I'd suggest getting some standard strength .38 Spl ammo, or even better some lightly loaded .38 Spl wadcutters. The use of these will allow you to concentrate on the basics of marksmanship without dealing with the increased flash, bang and recoil of the full strength magnum loads. Nothing says that you have to punish yourself, especially at the beginning. Besides that, the moderate & lightly loaded .38 Spl target ammo is going to be REALLY accurate, even in your .357 Mag. The wadcutters have practically no flash and recoil is just a bit more than a .22, where the "normal" strength .38 Spl ammo (I prefer 158 gr LSWC) is somewhat stronger but also pretty mild. Once you get used to the lighter stuff, you can move up the "food chain" to stronger stuff as your skill level increases. Even then, I'd imagine that you'd do as I do along these lines and still keep on shooting the milder stuff for just plain ol' target shooting and plinking, most of the time. Not all the time, of course, but just for your plain ol' paper punchin' and such.
And yes, I agree with the poster who suggests taking up reloading. If you want to put off reloading for a while, you might want to check out ordering some bulk reloaded .38 Spl ammo from the likes of
Georgia Arms or
MasterCast (I've use both of them in the past, both have been decent suppliers). You'll save a bundle on range ammo this way. FWIW, I still do business with Georgia Arms, I get my reloading supplies from them. I'd not hesitate to order again from MasterCast, but I don't buy reloads anymore since I restarted my reloading.