Well, if it wasn’t for the “enclosed arena” proviso in the OP, I would have suggested that the best armor is several miles of air. 
It’s off-the-shelf – heck, it’s on every store shelf in the world. 
I am just now realizing that you could apply almost all of this discussion to “What kind of armor would you need for a Man vs. fast Zombie fight?”
Articulated plate armor is winning the day. The only problem would be lack of general availability. Being that it’s custom made, a suit of armor made from carbon fiber/kevlar composite will be the answer. It can match the strength of the steel with much less weight. It would have to be a little bulkier all around to get the strength, but plate armor is pretty bulky already. You’d probably still want steel gauntets and helmet as weapons, and to make sure the monkey hurts himself going for your head. Winning this fight is near impossible unless you’ve had substantial training in the suit. Otherwise you will wear out before the monkey does, he’ll defile your prone armor clad body, and walk out to the cheers of his fellow simians.
Oh it’s based on a very old and probably inaccurate study that everyone quotes about how chimps are 8-10 times stronger than a man of the same size.(I think it was done in the 20’s) If I remember right a more recent and more scientific study put the actual strength difference as twice as strong as a normal human of the same weight. (Which apparently is weaker than a trained athlete.) Of course like you say, the big thing is they’ve got big sharp teeth and won’t hesitate to use them to bite off fingers, eyes, ears, and testicles/penis. (Oh and a male is on the order of 150-180 lbs so imagine how much damage a person with twice the strength and none of the restraint.) I mean all I’ve heard from all the chimp attacks support this point of view. (Since that old lady even had her hands bitten off but but didn’t have her arms ripped off.)
I think we’re in agreement though. Have armor that prevents him from using his teeth and that he can’t get off you easily. Probably the best bet is for it to include gauntlets with spikes on it so when you punch it you are effectively stabbing it. A few good shots to the ribs to create a sucking chest wound and he should be in deep trouble when he can’t breathe.
He doesn’t have to rip the arm / leg / whatever off though - he only needs to bend or pull it far enough to damage it so that it can’t be used anymore.
I don’t think it’s so hard to imagine enough pull strength to damage an arm beyone usefulness.
And given how good they are with tools, I think your simian opponent will be smart enough to work out that he has to get your armour off to get to the squishy bits.
I really shouldn’t make light of a horribly tragic event, but…
The takeaway here is clearly this: when bringing cake to a chimp compound, BRING ENOUGH FOR EVERYONE.
So, who would win between one hundred fast zombies and one hundred chimps?
The chimps would rip them apart, right?
Well yes and no.
The chimps would tear the zombies apart yes, but then they would turn into chimp zombies after feasting on tainted zombie blood.
I’m going with nature’s own body armor. It’s free, lightweight and highly available. I am of course referring to 3 miles of air. Granted, the soles of my feet would be vulnerable, but the little bastard would have to tunnel like crazy to get at 'em.
Honestly you can make decent articulated plate armor from plastic barrels, no trick high tech composites or elaborate tools needed.
http://darkvictory.com/html/catalog.html
As far as training, not really, decent armor is just something you wear. You will tire more easily due to the added load but thats going to be trivial against the exertion of a real fight or flight situation.
That atmospheric diving suit weighs over 1,000 pounds. I’m not sure you could even get the thing to fall over if you were inside it.
The devil is in the details. I missed that part.
Sign me up for one bomb suit.
Sheesh, a year later that thread is still provoking thoughts, and now body armor? Are our furry, terrifying forest friends plotting something I should know about? I’m concerned.
Wear a motorcycle helmet and some kind of crotch armor. Practice throwing punches and kicks wearing this armor. Chimps go for the crotch and face, they got no other moves. You will beat the chimp.
Will those punches be thrown before or after the chimp bites your fingers off?
A hand with no finger is still fist-shaped. Kinda.
Pray your hands can move quickly enough to break its neck at the beginning. No armor needed!