Beedrill

Beedrill lives up to its initial use in the original games flawlessly: an easily obtainable pokemon that's easy to raise and help bolster an early team. Sadly, its best role is nothing but a stepping stone to greater things in the game as any real collecting will yield better poison and bug types and leave Beedrill outclassed. On defense it's got a tiny bit of merit early on due to double-resisting Machamp's signature attacking set, but by that same token its entire moveset minus Elite Moves is hard-walled by Steel types.

The only real reason to raise a Beedrill is for Mega Beedrill.

Best PvE Offensive Moveset

• Bug Bite* and Infestation have roughly similar performance, with Infestation having better damage and Bug Bite better energy gain, though the legacy Bug Bite pulls ahead just slightly. 
• Poison Jab with Sludge Bomb is actually Beedrill's strongest moveset by a fairly wide margin. Poison Sting falls behind.
• X-Scissor is fast and furious, giving Beedrill a bug type set.
• Aerial Ace is fairly slow, but if you've just started and are desperate for fighting-type counters, you can leverage Beedrill's double fighting-resistance and use this. However, even many neutral matchups can out-damage Beedrill on this metric.
• Fell Stinger looks like a clone of X-Scissor, but it's substantially slower which makes it weaker in practice.
• Beedrill is a bad Bug-type attacker. It's an even worse Ground-type. Leave Drill Run alone.

Best PvE Defensive Moveset

• Poison Sting is the best Fast Move option available for defense, followed by Infestation.
• Poison Jab and Bug Bite* are the above moves, but worse when it comes to defense.
• Drill Run generally stands as the best Charged Move option due to its outstanding coverage.
• Arial Ace is solid overall.
• X-Scissor and Sludge Bomb should only be paired with Fast Moves of the opposite type, though their coverage is pretty similar so it's not a HUGE deal if you want to use them.

Beedrill has excellent Fast Attacks, but Poison Sting takes the cake with its superior energy generation, while still dealing decent damage. Poison Jab and Bug Bite are viable alternative options should more damage be preferred. Infestation is underwhelming

X-Scissor and Drill Run are two of Beedrill's Best Charged Attacks, with both moves having high DPE and solid coverage overall. Fell Stinger has okay synergy with Bug Bite or Poison Jab, but doesn't work well with Poison Sting's fairly low damage output. Aerial Ace is quite mediocre. Sludge Bomb can be used if stronger coverage against Fairies is needed. Return doesn't have much to target in terms of coverage.