no, they do the damage of the weapon, 1d3.
drop int and cha to 7 if you like. Archetypes use cha some, but the normal doesn't. and skills points use int. but other than that will for saves is all the combat effect you'll get from mental stats.
The knuckles used to use a monks unarmned damage dice but it looks like they took that out in one of the last publishing's. Sad, I used them as DR breakers.
The brawling enchantment for armor is a must. It is just a +1 cost but gets you +2 attack and damage and CMB on grapple. Light armor only, so theres an advantage over monks. Gauntlets of skilled maneuvers are a good buy to, you have a good CMB with your maneuver training, might as well build on it. Or you could get pliant gloves. Those are good for any melee.
This one is great for anyone. A Dusty rose ion stone is only 5000 gp for a +1 insight bonus to ac. That is less than what it costs to upgrade a +2 ring of protection or amulet of natural armor to a +3. However the really good part comes when you stick it in a wayfinder. If you aren't using the random tables that ion stone gets you a +2 to your CMB & CMD.
In case you haven't noticed I like using my flexibility feats for combat maneuvers. What is your build going to be like? What other kind of equipment you want to get depends on that.
First a Brawler gets Improved unarmed Strike, his unarmed attacks are lethal. No need for the weapon. The only way you would need the weapon would be to change the damage type, to say piercing, but you can take feats for that. Snake style does piercing, tiger style does slashing.
Int doesn't need to be high with level one giving you a int 13 when it comes to feats. Cha can be dumped as well, unless as CP said, your going for archetypes. Wis you may want to invest in as Brawlers have weak Will saves.
the Brawling enchant that goes on light armor is great, +2 attack and damage with unarmed strikes. Other then that, the ones you listed will work well.
That's just my 2cp
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Jingasa of the Fortunate Soldier is something you want on most characters, especially melee. +1 AC is good for the price(cheaper than the change from +2 to +3 Ring), Luck bonuses aren't too common, and ignoring 1 crit/day is literally a life-saver.
For stats, I find that you don't need an Int higher than 10, but having a 12 is nice for skills. Dumping Charisma shouldn't hurt too much, but consider finding some way to contribute socially even without a great diplomacy.
Brass Knuckles do 1d3, but do scale with the Brawler's 5th level ability (Close Weapon Master I think). Cestus has better stats though, and less restrictions.
The non magical elven chain and the magical celestial chain are both medium chainmail but count as light armor for anything. Including armor prof. So you can use it with your dodge bonuses and the brawling property.