There are a number of things you'll probably want. First and foremost, if you're going to use the PokéRadar, you can get it from Sycamore's lab after the Elite Four are beaten. If you want to do it with Chain Fishing, you'll need some kind of Fishing Rod - preferably Super, but Good and Old are also okay.
As far as Pokéballs go? We recommend the Dusk Ball or the Quick Ball. If you're playing at night, the Dusk Ball is always a quadrupled catch rate, whereas the Quick Ball only applies to the first four turns.
Similarly, you could use the Repeat Ball if it's a previously-owned species, or a Net Ball for Water/Bug Pokémon. Chain Fishers will also appreciate the Dive Ball. So, basically, if it gets a catch rate above x2.0, jump on it.
If you're planning on going for higher-level Pokémon, you need some other plans - most of the balls named above tend to fail on Pokémon at full health at Level 30+. False Swipe is an absolute must - be sure someone knows it as it can reduce Pokémon to 1 HP without KO'ing them. EVER. It kinda sucks on Ghost-types, though...
You'll also want someone to be able to use some kind of non-damaging status move. If you feel confident, use Sleep Powder, Hypnosis, or the like: it doubles the catch rate, but is temporal.
Thunder Wave, Stun Spore, and the like provide the usually-permanent Paralysis, but it's a x1.5 catch rate, 75% as effective as Sleep (and Frozen, but Frozen isn't induced without damage).
Basically status the Pokémon immediately, use False Swipe a bunch, reapply the status if it was Sleep, then throw a Pokéball. Pretty much the same tactics as catching Legendary Pokémon - and Shinies are way rarer than Legendaries, so go figure.