Even though Monk class has some nifty class features and better than descent skills, it is still a melee combatant class. So, strength is still the most important ability. If you can't hit and damage opponents well, opponents do not need to worry about you.
And even if you have maxed out your strength, you may still have hard time hitting opponents, due to crappy LA. So I don't recommend LA races without enough Str bonus, such as Aasimar.
So, I say either LA +0 race with high strength (Half-Orc or even Orc) or, some nice Large high strength race with acceptable LA, such as Centaur or Minotaur.