I'm convinced that the .308 is about the best pistol cartridge for someone new to bolt pistols, unless you find a stock XP in .221 Fireball.
Assuming you reload, it's dead simple to take any decent but cheap bullet (I used to love the Speer 130-grain HPs.) and seat it over a 60%-of-max charge of H4895. Recoil is tame and those heavy rams fall every time. I have more than one .308 pistol and that load is accurate in all of them with any bullet that's not so long that it won't be stabilized. In practice, a 180-grain Sierra match is about as long as you can go with a Wichita with such a light load. I've used everything from 100-grain Speer Plinkers to an old-design-and-no-longer-made Hornady 190 match with sub-MOA results.
As a bonus, with those loads the brass lasts forever.
If you really want to fire full-power .308 in a Wichita pistol, get a rear-grip. If you don't fight the recoil and just gently hold the pistol, the recoil will pick the pistol almost straight up and drop it straight back down. Yeah, there's some push but, subjectively, a hot .357 from a 4" S&W L-frame hurts more. Remember that when shooting a single shot, the whole idea of controlling recoil is moot. There's no such thing as a quick follow-up shot so there's no need to control the recoil. Don't try to control the pistol; hang onto it just hard enough that you don't let it escape your hand. Then let it recoil as high as it wants and enjoy the ride.
The Weatherby pistols are a different story. They're so expensive, such collector's items, that I can't imagine anyone actually shooting one. Plus, the triggers weren't all that great.
