I personally believe that Arcanine is a good staple for a Sunny Day team. Of course, there's the part about it being a Fire-type (STAB-boosted Flare Blitz coming off that Attack stat in the Sun is just scary). But Arcanine also gets access to Morning Sun, a fantastic healing move that recovers 2/3 of your health in Sunny weather. You can either go for a full-on physical attacking set with the attacks Flare Blitz, Wild Charge, and Crunch/Extremespeed, or try doing a special attacking set with Fire Blast, Solarbeam, and probably a Hidden Power move. Or you could go mixed, or you could even try running a more bulky set to play more on Morning Sun.
I believe it's far more likely that the offspring will have a certain ability if the parent also has it. Otherwise I think it becomes something like a 20-80% or 30-70% odds in favor of getting the same ability as the parent. If you only have a Wonder Skin Sigilyph, then I'd suggest using the multiple steps usually involved in breeding to get a Sigilyph with the desired ability (along with either the right IVs or right Nature, or a little of both) and then use THAT offspring to breed the NEXT Sigilyph; now that this one has the right ability, it'd be a much less tedious process than using one with the wrong ability and doing it over and over again against negative odds until you get the Sigilyph you want.
