The reason Humans (technically the whole United Federation of Planets) and Klingons were at odds in the TOS era is not fully explained. According to Memory Alpha, the issues between the two stemmed from a "disasterous First Contact," however, the exact details of what happened are not made clear. There are a few points where the different Trek series are apparently contradictory (or, at least, it requires some fan hypothesizing to make everything gel.) The bottom line, though, is that when Humans and Klingons first encountered one another, the result was a tense relationship that led to a "cold war" style era of hostility and skirmishing which lasted for about a century (depending on where you choose to draw the line in their timeline of events.)
According to the site, it looks like peace between the Federation and the Empire was ultimately and finally achieved by a breakdown in Klingon-Romulan relations, which led to the Klingons finally agreeing to join forces with the Federation against a "common enemy." This was after years of negotiations where the Klingons stubbornly refused to agree to any terms set forth by the Federation. So, it seems like the Klingons are really mostly interested in having someone to fight with, as long as they can be reasonably certain they'll win in the end.
Even if humans did not want to choose them as friends, it would be absolutely illogical and dumb to choose them as enemies.
Maybe the Federation weren't the ones who made that choice. It certainly seems like the Federation made several attempts to befriend the Klingons and atone for whatever happened during their First Contact, but the Klingons just weren't interested in making nice.
The last you want your enemies to be are warriors.
Certainly true, however, if the Federation simply capitulated to any overtly hostile regime they encountered (such as the Klingon Empire) in order to avoid making enemies out of them, then the Federation wouldn't last very long as a sovereign power in its own right. Sometimes you have to take a stand in your own interests, even if it means making enemies out of someone you'd rather not be enemies with.
Finally, to address the question of choosing to be friends with a Klingon "because they're honourable and loyal," it really does bear repeating what Miltonaut said in the comments to the question: Klingon honour and Human honour are two very different things.
I can't find the exact quote right now, but in the latest "New Trek" movie, there's a line about how Klingons would ambush a civilian convoy, slaughter everyone and then be lauded as "honourable warriors" upon their return, simply because they won. Granted this was spoken by a Federation crewman during the time when Federation-Klingon relations were at the height of their hostility, so there was probably some exaggeration there. However, there are also plenty of other examples throughout the various TV series where Klingons are shown taking a more violent path than is necessary to achieve their goals.
Their version of "honour" and "glory" are very different than ours. Even asking them to stand down for your sake could easily lead to them declaring you "dishonourable" - at which point their "loyalty" will shift away from you. So, "which one to be friends with" is not really as clear-cut a decision as it may seem. Worf was something of an outlier in this regard, having been raised among humans. He still adhered to the idea of honour and loyalty, but those definitions were strongly influenced by human culture.
(Personally, I think I'd choose Vulcan. Even choosing a Ferengi wouldn't be so bad, as long as you're careful about any monetary transactions you agree to.)