Generally, what you want to look at as a monk is energy regeneration. Both Mo/N and Mo/Me provide for this need, with Offering of Blood (E) for Necromancers and Energy Tap or Energy Drain (E) or energy-gaining interrupts for Mesmers. Mesmers also have access to Hex Breaker and Illusion of Weakness, but both of those are generally better in PvP than PvE. Mo/E can provide you with limited energy recovery in the form of Glyph of Lesser Energy and Glyph of Energy (E), though I don't generally recommend the elite.
Other than energy recovery, there are a few useful options for monks with a secondary profession. Mo/R provides access to defensive stances or a pet. While Mo/E shouldn't be wasting its energy on costly Elementalist spells, you can get Earth Magic enchantments and wards to boost up your AL or provide evasion and take less damage. At the very worst, you could use Lava Font or Firestorm to make PvE opponents flee from you

Mo/N could farm with Spiteful Spirit or use many interesting curses, though again, you will most likely be expected to just heal. Mo/Me probably offers the most options with its stances and energy recovery. And as mentioned above, Mo/W will have great success in farming due to a certain build that's floating around.
If this is not your first character, just pick a profession you don't already have on another character to unlock the skills for PvP. If this is your first character, go with Elementalist because that's my favourite

In any case, do all the "introductory" profession quests (the ones where you get free skills) in pre-searing to squeeze out more xp from it. By the time it starts to matter what your secondary is, you could probably do the quests in the desert to change it.