Don't forget you also get TWF and Improved TWF via brawler's flurry. Only with close weapons and unarmed strikes but I'm guessing you use the latter a lot.
Here's a simple combo. Snapping turtle style, snapping turtle clutch and combat style mastery. Snapping turtle clutch gives you the ability to start a grapple when someone misses you and combat style mastery lets you swap between it and pummeling style easily.
Or for all-out grappling mastery: greater grapple, rapid grappler and dedicated adversary.
For a different combat maneuver: tripping wants improved trip and preferably greater trip and fury's fall. If you have +2 dex or less, try dedicated adversary again in place of fury's fall.
Or for another: improved overrun, greater overrun and maybe charge through might be fun.
If you're up against a big enemy and don't want to grapple it, maybe improved & greater dirty trick, maybe equipment trick (smokestick) or maybe dedicated adversary.
When blinded or against invisible enemies consider blind-fight and blinded blade style.
Sometimes you just want punching damage of course. Dedicated adversary, martial focus, maybe pummeling charge so you can get in a full attack easier are feats to consider here. If you have 3 ranks in swim and won't want/need to charge then shark style may be on the cards.
Sometimes you'll need to delay dedicated adversary until you're sure who you're fighting, and sometimes you'll want to delay or skip a feat or two for faster buffing.
This is obviously not a complete list of all the good things you could do with 3 flexible feats. That would be ... long.
The Soulblade, Ghostslayer, and Rat Catcher feats are useful to know about since they'll provide your Brawler with ways to deal with enemies and situations that they might normally have no way to handle.
There's other styles which may be useful sometimes, sure - e.g. dragon style has its points when you need to deal with difficult terrain or for a little more damage. Mostly they're going to be situational though. Also I don't know whether you have the required ability scores or skills. Panther style/claw requires Wis 15 for example, dragon style requires 3 ranks in acrobatics.
Immediately I think of cleave and great cleave (if you're spontaneously surrounded)
Branch pounce always seems like a fun tool to have for martial flexibility.
You could also get outslug style, outslug weave, and lunge. It helps you be more mobile, and potentially full attack someone from ten feet away. The AC and damage boost is just gravy.
As another option there is spring attack. Unfortunately I think you're one feat short of improved spring attack.