This particular bullet mould was made by BRP and throws .351" with wheelweights. Then they're patched up with drafting vellum to .360" and run through a .359" Lee push through die. But special bullets are not required, any 35 cal. bullet cast pretty soft can be patched with thin paper and then sized, using wax for lube. I use the Lee 358-158-RF patched with tracing paper and sized to .359" as well, and it works just fine unless you harden the bullets. With paper patching there's no need for really hard bullets anyway, especially at the speed a 357 max will generate.
All the calibers you list should work great with paper patching. Depending on what throat you have in the 45-70 you might have to seat the bullet pretty deep in the case. But the SAAMI throat for the 357 and 44 mag are just perfect as is, a big funnel that lets you seat the bullet out pretty far. As for diameter, as big as will easily chamber is the way to go. Just make sure your belling die is big enough so you have adequate neck tension, but not too tight to tear up the patch.
As for tools, a paper cutter is a must. A hot plate for drying the patches really helps. A push through size die for sizing, and a cigarette roller for rolling them on. Pretty much all you need. No lubrisizer, no gas checks, very simple. It took me about a year to figure out how to really make it work, my first attempts were dismal. But I slowly learned how to make it work, and now I am seeing a whole world of shooting open up to me that was unavailable before. The performance these things are capable of is far beyond what is possible with grease grooved bullets. For example, I have finally gotten my 375 Taylor to throw a 265 gr. bullet at 2600 fps and hitting a 6 inch disc at 385M most of the time is not hard. This kind of thing was simply not possible until I learned how to paper patch properly.