Regrettably one cannot obtain a Shiny Jirachi without hacking so that is a no-go for you. As for a move set, that's up to you really. Jirachi has 100 in ever stat so you can make a Special sweeper with either a Modest or Timid Nature investing EVs into Special Attack and Speed, a Physical Sweeper with Adamant or Jolly Nature with investment in Attack and Speed, a Mixed Sweeper with investment in both Attacks and Speed, a Physical or Special Wall with investment in HP and the apropriate Defense, a Mixed Wall, or a Bulky Sweeper with investment in HP and one or both Attack stats.
By the sounds of it, Bulky Physical Sweeper is what you seek so you would want an Adamant Nature, 252 EVs in Attack and HP, with the remaining 4 EVs in either Defense, Special Defense, or Speed. Wish and Thunder Wave are good support choices while Zen Headbutt takes advantage of Jirachi's Psychic STAB. The last move I'd throw on this set is Iron Head which can be tutored at the Battle Resort in ORAS. Item wise, go with Life Orb to make the most of your attacks. The recoil damage can be easily healed with Wish. I hope that helps you in some way. Of course since the Jirachi event is now over, you're limited to what you can do based on the IVs and Nature of the ones you got so my advice may end up being moot anyway.
