I realize this is a slightly unconstrained question (what qualifies as best?), so let's constrain it a little.
In Generation V we've reduced the number of HMs to 6. Now given I can only stick 4 moves on a Pokémon, let's first constrain this problem by limiting the moves to HMs 1-4 (Cut, Fly, Surf, Strength). Now, 3 out of those 4 are physical moves, so let's prefer Pokemon with high Attack. Finally, let's preferentially select for Pokémon we encounter earlier (rather than later) so we can take advantage of our mule of longer.
To summerize:
Best HM Pack Mule that:
- Can use Cut, Fly, Surf, Strength
- Has a high Attack
- Occurs fairly early in Pokémon Black and/or White
Best Answer
The only HM you need to complete the main storyline of Black and White is cut, and this is a one-time event (you need to Cut a tree down in the Dreamyard to progress the storyline). Because of this, other HM moves only allow access to hidden items or for convenience. The main HMs people use are Surf and Fly, and Ducklett / Swanna can both learn the two moves.
Ducklett can be found as a shadow on the Driftveil Drawbridge, and Swanna on the Marvelous Bridge. (I believe you cross the Driftveil Drawbridge before even obtaining Fly or Surf.)
If you want a Pokémon that can learn Cut and Strength, Patrat is available early in the game and can learn Cut. When it evolves into Watchog, you can teach it Strength. (No Pokémon in Gen V can learn all four moves you listed.)