Your team would probably cover all the types except:
- Electric (for that you need either a Dig / Earthquake user or a Ground type)
- Dark (fighting type or Brick Break / Drain Punch user)
- Normal (Again a fighting type)
- Dragon (unless you have Ice Beam for Slowbro)
- Flying (same as Dragon)
- Ghost (unless you have Shadow Claw for Ambipom)
- Psychic (same as Ghost)
So the main threats are the first three. You need either a Fighting or a Ground type.
Since PP of Drain Punch and Close Combat is only 5, I would recommend you use Brick Break along with these.
Earthquake is available only in the later part of the game, so use Dig for time being.
Pokémons which can learn the above moves are Poliwrath, Heracross, Machamp, Pinsir, and Hitmon Trio (not Dig).
Since you need:
- No two Water types,
- No trading,
- STAB for either Fighting / Ground type moves,
You are left with Heracross, Pinsir and Hitmon Trio. Out of these, Heracross is availble in early game. So I recommend you to choose Heracross.
Heracross @ anything
Nature: not -Atk and -Spe
- Brick Break
- Mega Horn
- Close Combat
Also, I recommend to give
- Ice Beam TM for Slowbro
- Shadow Claw and Dig TM for Ambipom
Hope this helps :)