The solvents you have to watch are the ones containing ammonia. Ammonia is an effective copper cutter, but the the rounds you're shooting won't leave significant copper fouling in the bore the way a high velocity rifle might. The problem with ammonia is that as it evaporates, it corrodes the steel under it. Yet you can plug the chamber, fill a bore with ammonia, seal the muzzle to prevent evaporation, and leave it overnight with no harmful effects to the bore. Frankly, its simpler to use Sweets as directed, or better yet, an ammonia free, foaming bore cleaner, like WipeOut to get rid of copper fouling.
For your purposes I'd use Hoppes #9 just because I like the smell, and any light machine oil to work through the bore, then patch dry. Your autoloaders might appreciate a small dab of grease, on those moving surfaces that show wear. I use Lubriplate 130-A, which was formulated for use in automatic weapons for the US military, I got mine from Brownells. A can will last many years, so be sure to keep it well sealed and uncontaminated. Use one piece cleaning rods like Dewey or Tipton, use only high quality bronze brushes if you have stubborn lead fouling as sometimes occurs in a .357, be sure to use a brass jag to push the patches through, and patches should be 100% cotton and cut to the correct size, although large patches can be punched off center, and larger patches can be used with small jags. An M-16 style steel jointed rod is useful for field use, and the handle section with the short accessory rod is useful for handgun barrels and revolver cylinders. You might prefer a .17 caliber rod for use with a .22 brush for your rimfires, and the .17 jag will work with an oversized patch. A nylon parts brush, or even a toothbrush is useful for cleaning small parts, bolt faces, and bolt recesses.
When you're faced with a lead fouled bore, use a bronze bore brush dry, no solvent or oil, and push it all the way through the bore. Some folks prefer to remove the brush prior to pulling the rod back, so as not to pull loose fouling back into the action. After 20 or so passes, use a couple of patches wet with dime sized stains of solvent to push out any loose fouling, pushing each patch right through the bore. Then run a dry patch or two right through the bore to remove the solvent. If the bore is badly fouled, you may have to repeat this procedure several times. Once the lead fouling has been removed, and the bore is dry, put a dime sized stain of oil on a patch and work it back and for through the bore advancing an inch or so at a time, then patch dry with a single patch or two pushed right through. Powder fouling alone is easily solved with a dime sized stain of solvent on a patch, work the patch back and forth through the bore, then patch dry as above.
When cleaning be sure not to allow solvent or oil to enter the inletting of wood stocks. This will soften the wood and destroy the accuracy of your rifle. You should seal the inletting of your wood stock with an appropriate wood finish like True Oil or boiled linseed oil.