trentonjoe
Explorer
If you're starting at higher levels, then there are times when multiclassing in one order is clearly better than another (like your rogue/monk example). Usually the most important part of the order, though, is what your character is like while you're leveling. If you want to get to rogue 5 / monk 5 eventually, the main question (for me) would be whether I want to spend the first five levels playing a monk or a rogue.
The main exception I can think of to this is if you're mixing something like fighter and wizard. Even if you'd rather start out mostly as a wizard, the hit points at first level and proficiency in constitution saves (for concentration) can make a strong argument for taking your first level in fighter.
This makes sense. The only things that can be effected by the order are:
Hit points
Saves
Skills (thieves still get more to start right)
Armor/Weapon Proficiency
right?
If you need one of those things make sure your first class has what you need.