Sniper works very well with the dual-STAB combo of Angle Stab and Cross Poison. Beedrill can run several coverage moves with a high crit chance including Drill Run for Fire and Rock types, Drill Peck for Glass types, and Stone Edge for Flying, Fire, and Glass types. For the fourth move, Beedrill has access to high-power moves like Giga Drill Break or Outrage. Both have negative effects, but Beedrill probably won't be staying in for long enough to experience them.
Though Beedrillite makes sense to use for a higher attack and slightly higher speed, the mega could probably be used elsewhere on the team to greater effect. As such, Beedrill can take advantage of the high crit-rates of its moveset by equipping a Scope Lens, which Sniper can use to gain an attack boost similar to if it were to use its mega form. Expert Belt is also nice due to an immediate power boost on Super-Effective hits with the drawback of losing out on crits.
Access to high-crit chance moves and Angle Stab's auto-crit leaves no question that Sniper is Beedrill's best ability. Sniper gives all crits an extra 50% power, which boosts Angle Stab's base power to a base 270, hitting harder than Explosion clones like Final Sting. Cross Poison becomes equally as terrifying, with a maximum 360 base power and a chance to cripple physical walls with status.
Though Beedrill hits like a freight train when it crits, its speed is average and its defense and HP are poor. Faster Pokemon with access to Physical moves that attack Beedrill's weaknesses will most likely OHKO or force a switch-in. Additionally, a Pokemon with Battle Armor, such as Armaldo, can wall Beedrill and threaten to set up in its face or take it out without any worry of retribution.