I've never played BW and I might never play them in the future, but I worked very hard on this team and I thought it would be a waste of my time if I didn't share it. The whole team can be assembled before defeating Clay, and has a super effective STAB attack against every major opponent except Burgh's Dwebble. The only problem with this team is that it requires at least two HM slaves. Please note that I didn't plan for post-national Pokedex opponents.
-tackle -> arm thrust -> hammer arm
-ember -> flame charge -> heat crash -> flare blitz
Notable NPC battles against fire-weak Pokemon: Bianca, Burgh, Clay (again, don't use Pignite against Clay), Brycen, Bianca, Grimsley, N (I'd suggest you not use Emboar against Carracosta because it knows waterfall), Ghetsis
Notable NPC battles against fighting-weak Pokemon: Cress, Cheren, Lenora, Charles, Clay (I'd suggest you not use Pignite against Clay because his Pokemon know bulldoze), Cheren, Brycen, Bianca, Cheren, Grimsley (I'd suggest you not use Emboar against Krookodile because it knows earthquake), N, Ghetsis
As far as I know, this is the only way to get any fighting attacks before defeating Cress, who uses a Lillipup. Because of this, if you want to use fighting attacks on Lenora's Pokemon, you need to evolve Tepig as soon as possible. After you have a Pignite, you can keep it a Pignite until it learns flare blitz at level 52.
-vine whip -> seed bomb
Notable NPC battles against grass-weak Pokemon: Cheren, Cress, Cheren, Charles, Clay, Cheren, Bianca, Cheren, Shauntal, Grimsley, N, Ghetsis
You can get Pansage before the second battle against Cheren. I'd suggest you evolve it after it learns crunch, but you can evolve it anytime as long as you have a leaf stone and a move reminder to teach it seed bomb.
-bite -> assurance (if it suits you) -> crunch
-sand tomb -> dig -> earthquake
-mud-slap -> strength
Notable NPC battles against dark-weak Pokemon: Skyla, Bianca, Shauntal (I'd suggest you not use Krookodile against Shauntal's Jellicent because it knows surf), Caitlin, Ghetsis
Notable NPC battles against ground-weak Pokemon: Elesa, Charles, Clay, Cheren, Shauntal, Grimsley, N (I'd suggest you not use Krookodile against N's Carracosta because it knows waterfall), Ghetsis
You can get Sandile before defeating Elesa. Unlike all other ground Pokemon in the whole game, Krookodile gets STAB for crunch, which lets it land even more super effective attacks than it already does. You should evolve your Sandile at level 43 after it learns earthquake. You can then evolve it into Krookodile at level 44.
-spark -> wild charge (TM found in Victory Road)
-pursuit -> light screen
-double team -> encore
Notable NPC battles against electric-weak Pokemon: Charles, Skyla, Cheren, Bianca, Cheren, Shauntal, Caitlin, N (I'd suggest you not use Emolga against N's Archeops because it knows stone edge)
Notable NPC battles against flying-weak Pokemon: Bianca, Grimsley, Marshall
Of all the electric Pokemon in Unova, Emolga comes with the best second type and an exceptionally powerful STAB attack in acrobatics. You can also teach it roost, which is very useful in things like the Battle Subway and even better ingame. If you don't want to wait until Victory Road to get a good electric attack, you can use a special set. However, this involves grinding a Woobat until it learns air slash, and then breeding it with a female Emolga, so I wouldn't recommend it.
Ability: ice body
-icy wind -> ice beam
-acid armor -> hail
Notable NPC battles against ice-weak Pokemon: Clay, Skyla, Cheren, Bianca, Drayden/Iris, Cheren, Shauntal, Grimsley, Caitlin, N (I'd suggest you not use Vanilluxe against N's Archeops because it know stone edge), Ghetsis
This is the last member and only special attacker on the whole team. Vanilluxe is faster than Beartic, has better defenses than Beartic, can be obtained earlier than Beartic, and has a much less stupid design than Beartic. You don't really need to delay its evolution, because it learns all its good moves before evolving. (unless you want mirror coat early. you'll have to delay evolution for level 44 for mirror coat)
Good HM slaves to go with this team include Basculin (cut, waterfall) and Ducklett (fly, surf). Neither can learn strength, so I suggest teaching strength to Krookodile.
If you like catching a lot of Pokemon, replace Simisage with Leavanny as soon as you can get Sewaddle.
-bug bite -> swords dance or x-scissor
-razor leaf -> leaf blade
-protect -> false swipe
Notable NPC battles against grass-weak Pokemon: Charles, Clay, Cheren, Bianca, Cheren, Shauntal, Grimsley, N, Ghetsis
This is the only Pokemon I could find that's on the Unova local Pokedex and can learn false swipe and a sleep-inducing move. Sewaddle learns all its good moves before level 20, so you can evolve it into Swadloon as soon as you want. Swadloon learns all its good moves before level 21, so you can evolve it into Leavanny whenever you want. If you manage to do it before level 37, you don't need to spend an extra heart scale teaching it leaf blade.
This answer took longer than I thought.