Interesting question and I have not really been surprised with the answers. Most is seems like either the AK or M1. Good choices, but their reasoning is often left out.
When you consider what a battle rifle has to go through to be acclaimed "best" they are all remarkable, with a couple of exceptions.
With that said, I would like to throw my idea into the quest for the best.
I think first of all you are trying to compare apples to oranges. By that I mean you are comparing bolt actions to semi and full auto's. I really think they should be separated. One answer did with the offering of the Brown Bess, and his thinking was good on the subject. I would have to say he is correct with the proviso that you only compare it to other front stufers. They could not begin to win a battle against even the worst of the rifles you have on you list.
As far as the bolt action rifles you have listed, it really comes down to just two. The Lee Enfield is one of the greatest and for sure was issued a long time to a lot of troops and decided many battles. If I may include all mauser 98's and not just the kar98, then it too requires a place right along side the Enfield. If we must consider only the kar98 then it drops in its value as a battle rifle. Those two are almost neck and neck, but I would place the mauser 98 a half a nose ahead of the Enfield, and would not argue with anyone who thinks they are reversed.
On the other hand the Mosin Nagant is not to be put out of the race either. It is a very superior firearm. To place then in a 1,2,3 order, I would put them Mauser 98, Lee Enfield, and Mosin Nagant. They are all three great firearms, and I would not want anyone using any of the three against me.
As for the semi-auto's that is much easier. First, if you consider which one can be dropped into a mud hole and fired, or into a pile of sand and fired with the fewest problems, then the AR has to be placed on the bottom of the list. The only thing the AR has going for it is its inherant accuracy. But others are capable of sub minute accuracy as well, but usually not right out of the box.
Now which one can endure that kind of punishment and still fire. For sure we again come down to just two. First I want to put all the M1 and variants such as the M1A and M14 into one family and say it is tops, with the M14 being the best of the three.
Next, no one can argue the AK (considering both the 47 and 74) and its variants has passed the test as well. It has been issued longer and to more soldiers than any of the semi autos listed. It is still being issued 60 years after its invention. (I believe only the 1911 was issued longer.)
So again to list 1,2 it would have to be the AK first and the M1 family second (with M14 being best of family). Again, I would not argue with anyone that would reverse the two, they are so close.
You have put together a great list, and I would like at least one of each.
And so the argument continues.