There really isn't a standard weight/size for .577 that will be a go to when it comes to these kinda things. You'll have to measure out your barrels lands/grooves and size your bullets accordingly, anything beyond that will be further experimentation.
I've been running a Pedersoli P53 and my barrel measured out to .587 rather than the advertized .577. My gun ended up really liking a 620 gr shallow skirt slug that packs a fair wallop with around 64 grains of 2fg. Tried more traditional 420gr minies but never could get them to shoot straight.
Good luck! Once you figure out what your gun likes it's a lot of fun ahead.