I'm planning a Rogue/Monk character, and I'm planning on being a highly mobile Monk who moves around the battlefield a lot, trying to get as many attacks as possible.
The Rogue subclass is going to be the Swashbuckler, mainly for the Fancy Footwork feature:
During your turn, if you make a melee attack against a creature, that creature can’t make opportunity attacks against you for the rest of your turn.
I do not know for certain which Monk subclass, but I am thinking of either Drunken Master for the free disengage when using Flurry of Blows (from Tipsy Sway) or Open Hand for the Open Hand Technique benefits.
I was planning on starting as Rogue and taking it to as least level three (for Fancy Footwork) then mainlining Monk to at least 5th, before going back to Rogue until at least level 12-13.
One of the ideas I had was to take the the Martial Adept feat, to add some variety to my actions.
I know some of the Battle Maneuvers aren't synergistic with monk abilities, like tripping, because Monks can eventually get Stunning Strike. The most important thing for my character is to be free to move between enemies, getting in as many attacks as possible, without being stopped or interrupted/killed.
Which maneuvers help with this the most?
The obvious candidate: Evasive Footwork
This is probably the best one on the list. A good roll on the superiority die can mean you are nearly untouchable for the duration of your move.
Honorable mention: Parry
If you do get hit while weaving between enemies, Parry allows you to reduce that damage a bit.