The first War correspondent I know of was The Times journalist William Howard Russell who covered the Crimean War from 1854 to 1855.

Combine his reports with the fact Roger Fenton was also there, photographing the battlefields and figures of the War, and the Crimeanl War contains not only one of the first war correspondents but also one of the first war photographers (though emulating Fenton would get you fired from any publication, his Valley of the Shadow of Death photo was set up.)

WH Russell went on to cover parts of the Indian Rebellion of 1857, he was present in Washington at least during the first years of the US Civil War.

Some of William Howard Russell's report on the Charge of the Light Brigade is here on wikisource But if I find a better source for some of his writing I'll throw it in here.

The big bonus of having people like WH Russell on the ground was the actual accuracy and human side of the reporting. Prior to war correspondents, papers would only give the official reports on wars and battles, which as a rule aren't much interest to readers and, while they no doubt give a great view of the big picture strategically, don't really report much on the plight of the common soldier.

Hope this answer helped, my knowledge on this sort of thing is more journalistic than it is historical, really.

I can't tell you the exact date when journalists first started going to battle exclusively to record events but i know foreign observers were present Croatian–Slovene peasant revolt of 1573. So it is fair to say there was some level of unbiased foreign historical recording as far back as the medieval era. Generally speaking though History was always written by the victors right up through until very recently.