Your choices for an Electric type are Manectric, Plusle, Minun, Magnezone, Electrode, Pikachu-Cosplay, Raichu, and Lanturn. From experience, Plusle, Minun, and Electrode aren't very good, Raichu comes a bit too late, and there are better Water types than Lanturn. As you said, this leaves the list of contenders at three: Manectric, Magnezone, and Pikachu-Cosplay.
Manectric
- Electrike comes at a higher level than Magnemite, but lower than Pikachu-Cosplay
- Special Attack and Speed both over 100
- Has a Mega Evolution
- Evolves earlier than Magnemite
- Learns moves like Wild Charge, Signal Beam, Flamethrower and Overheat
- Movepool is pretty bad without breeding
- Medicore stats in everything except Special Attack and Speed
Magnezone
- Electric/Steel is one of the best type combos
- Higher Special Attack and Defense than Manectric
- Respectable Special Defense, but mediocre stats in the other categories
- Learns moves like Flash Cannon, Discharge, Volt Switch, and Signal Beam
- Like Manectric, it has a pretty bad movepool
- Found at the same time as Electrike but at a lower level
- Evolves later than Electrike
Pikachu-Cosplay
- Comes earlier and at a higher level than both Electrike and Magnemite
- Gets a free powerful move in three of its forms: Flying Press, Icicle Crash, or Meteor Mash
- Learns moves like Thunderbolt, Nuzzle, Strength, Iron Tail, and Quick Attack
- BoltBeam with Pikachu-Belle is an amazing combo for the early game
- Very poor stats
- Usefulness drops off quickly due to aforementioned poor stats
- Will be outclassed later on
- You have to participate in a Contest to get it, which can be a waste of time
The best option is Magnezone. Magneton is acceptable until you get to the New Mauville electrical field (it's worked very well for me in the past), but it coming at such a low level can be problematic. However, due to the EXP Share, it'll catch up to the rest of your team quickly. If you want to use another Electric type to supplement Magnemite before it's usable, use Pikachu-Belle or Pikachu-Libre. As you said, BoltBeam is amazing, and Icicle Crash makes Belle arguably the best equipped at dealing with early-game opponents. Libre, however, is much better equipped to deal with Wattson's Magneton due to Flying Press.
Here's a set for Magnezone (All you need for the Pikachus is Electric STAB + Icicle Crash/Flying Press):
Magnezone @ Magnet
Ability: Sturdy
- Thunderbolt / Discharge
- Flash Cannon
- Tri Attack
- Thunder Wave / Volt Switch / Supersonic
Good luck with your playthrough!