The K frame S&W and current-production Colt double-actions are compact, light, and easy to carry while still shooting much better than J frames, LCR's, and Kimbers which are too light and awkwardly small to shoot easily and comfortably. The little guns are ok if you back off on the power factor, but you're expressing an interest in range-time and not carry, so I would suggest stepping up even from a K frame/Colt Cobra.
The two big advantages you get stepping up to a L frame or GP100 is weight and barrel length. The weight is important when shooting a higher power factor. When the barrel length exceeds 4" (to 5", 5.5", 6" and beyond), even the .357 produces big energy for a handgun. My 5.5" .357 can produce more than double the energy of that of popular 9mm self-defense loads commonly shot out of autoloaders with reciprocating slide mass and recoil springs that reduce the recoil velocity. In a revolver, the only thing reducing recoil velocity is the gun's mass.
S&W doesn't currently produce a K frame with more than a 4.25" barrel, and while the current K frames are easily stout enough in all ways to handle a high volume of maximum .357 Magnum loads, their ~36 oz. weight doesn't make this a pleasant endeavor. The full underlug on L frames and the GP100 not only add mass, but they also add it where it tends to reduce muzzle flip the most. Porting or compensating a K frame can also reduce muzzle flip, but it won't add the mass the reduces recoil velocity.
.357 Magnum in particular is benefited tremendously by increased barrel length. I've measured a consistent 40 fps difference just between a 5" and 5.5" barrel (same b/c gap). Going from a 4" to a 6" barrel can add hundreds of fps with no additional pressure. If power factor or energy doesn't mean anything to you, then just shoot a 4" K frame .38 Special. It can't be beat. But if you do care about power then there's no replacement for a longer barrel and you'll appreciate a gun with more mass.
Venturing into the big bores, your ammo and component costs will increase substantially. I would suggest a .38 or .357 to learn the double-action trigger and reloading and then a big bore should you wish. While there are L frame and GP100 sized guns in .44 Magnum and 10mm, big bore double actions are generally N frames or Redhawks. I can't speak from enough experience with these to offer good advice, but I would suggest that a .454 Casull or .460 S&W is a poor platform to learn double-action revolver on, even if you shoot more economical and lower recoil .45 Colt. The mainsprings on those guns have enough strength to strike rifle primers and that makes the triggers even harder than what you'll have to overcome to shoot any double action.
