If you're playing Red/Blue, then Pikachu can be caught at levels 20 and 24, and will have Quick Attack, Thunder Wave, Thundershock, and Growl. Not super ideal, but you can teach it Thunderbolt with the TM you got from Lt. Surge.
If you're playing FireRed/LeafGreen (which I assume you are based on the levels you gave), then Pikachu will have Slam, Double Team, Quick Attack, and Thunder Wave at level 22 and 24, and Thunderbolt instead of Thunder Wave at level 26. So even if you do catch a lower-level one, it'll only take 2 to 4 levels for it to learn Thunderbolt.
Whether these movesets are good or bad is really up to you, but Pikachu isn't exactly known for having the widest movepool there is, so I would argue that Thunderbolt is all you really need.
PIkachu Gen 1 Learnset
Pikachu Gen 3 Learnset