Off topic, your group should check out a VTT, I use roll20, let's my group game from 5 different states every week.
Jabbing style and crane style? You know you can use only one of these at once, at least unless you take a dip in master of many styles monk?
Close weapon mastery is useful if you find a magic weapon of that kind which is better than whatever amulet of mighty fists/handwraps or whatever you might have, but it doesn't otherwise make a cestus better than your brawler's fists. You might possibly use a waveblade if you want to go crit-fishing though.
Don't forget power attack as a feat (unless your group uses a feat tax reduction system like Elephant in the Room, but since you said no 3rd party I'm guessing not?). Whichever style feat you like best, pick up the subsequent feats too, jabbing dancer/master if you go jabbing style for example. And any prereqs for those, mobility is required for the jabbing line.
If you do decide to go with more than one style make sure you get combat style master.
Look into the Hinyasi brawler with shikigami style.
Is this level 10 again? The feats seem to stop there.
Pummeling style is fairly pointless for an armed character. Also the shield champion gets some abilities which are not purely DPR and it seems a shame to leave those high and dry. A few feats on a combat maneuver are not a waste here IMO.
With brawlers you can pick up feats on the fly, so with my brawler I focused on getting pre-reqs, like combate expertise, that alone allows me to take most combat manuever feats on the fly, as far as combat styles sadly o ly one...UNLESS
Martial focus-close weapons
Weapon style mastery
This allows you to use 2 at a time, as long as one of the fighting styles has weapon focus as a pre-req
One of which is outslug style
I recommend it :)
But you can always switch between styles if you want, and even pick up niche styles when you need them :)
But for the rest focus on basic combat feats, and pre-requisites :)
Also, as long as your doing dirty fighting look at quick dirty trick, dirty trick master, and superior dirty trick ;D
With brawlers you can pick up feats on the fly, so with my brawler I focused on getting pre-reqs, like combate expertise, that alone allows me to take most combat manuever feats on the fly, as far as combat styles sadly o ly one...UNLESS
Martial focus-close weapons
Weapon style mastery
This allows you to use 2 at a time, as long as one of the fighting styles has weapon focus as a pre-reqOne of which is outslug style
I recommend it :)But you can always switch between styles if you want, and even pick up niche styles when you need them :)
But for the rest focus on basic combat feats, and pre-requisites :)
Or you can dip one level into master of many styles monk to grab fuse style.
Which works really well as a hinyasi specalializing in improvised weapons, play as a half orc for the favored class bonus, grab some monk robes, and at level 13 using pummeling style and shikigame style you can charge and make a full flurry doing 8d8 plus modifiers per hit.