For target I would recommend a Ruger 22 semiauto military target. extremely accurate, quite, and really cheap to shoot,
Exactly. You don't shoot a .357 as a beginner, you graduate to a .357 after having mastered the basics of shooting.
You are just talking about target shooting, right? The .22 is still the King of competitive marksmanship and target shooting. There is every reason to start with a .22.
All of the masters recommend working with .22 to correct bad habits that may start to creep into your technique, because that's where you should have mastered the basics to begin with. Progressing to a 9mm/.40S&W/.357 from a .22 is a whole lot easier than progressing from nothing.
Recoil matters, when you're trying to learn fundamentals it can be nerve rattling, which invariably causes undesirable psychological responses, which invariably affect your shooting. Many bad shooters don't know why they're bad shooters, its often because they have developed poor habits and technique due to the inherent stresses of beginning with too big of a gun.
Shooting a larger caliber handgun is not a cheap hobby. I used to shoot 300-400 rnds (combined) of 9mm and .40S&W every weekend, and at $10.00 (average) per box of 50 (including tax and shipping), that's $60-$80 plus $10 an hour range time. For the same $60, you can buy about 1500rnds of mid-grade .22 ammunition (figuring $2.00 per box of 50). And let me tell ya, shooting 300 rnds of .22 is hardly noticable, but you WILL start feeling every round of 9mm/.38/.357/.40 after about 250rnds, depending on the caliber, the gun, and how long you've been shooting (especially if you opt-out of using a Super-Loader - wretched loading thumb syndrome).
But it doesn't matter what you start with if, you aren't learning proper fundamentals, your shooting will suffer and your slow progression will lead to frustration and a barrier to enjoying your day at the range. Check your local gun clubs or ranges for basic shooting instruction and take a couple courses.