It doesn't get much more legit than NGC. They do not offer a "guarantee" of authenticity, but they won't slab a coin that they believe to be fake.
NGC is a very well known coin grading company and it is, for the most part, very trusted among most members here on CoinTalk. I have never sent coins to be graded there, but I know others that have; and from what I've seen, NGC usually does a good job grading and attributing coins.
I trust NGC for grading. But the thing one has to remember is that they do not guarantee authentication and there have been mistakes in the past, albeit very few and far between.
NGC does a very nice job with grading Roman imperial coins. But since I like my coins raw, I don't have a lot of them. I do have a couple of pieces that dealers crack out of NGC holders and sold. NGC is the leading grader from world coins. I think that they do a better job than PCGS in that area. PCGS is better for U.S. coins, in my opinion.
NGC Ancients has a very good reputation for ancient coins. NGC Ancients doesn't guarantee authenticity of ancient coins. But, they won't slab an ancient coin which they believe is a fake. They seem to be excellent, at identifying fake ancient coins. However, it seems like, anyone can make a mistake. For medieval and modern coins, I don't know what NGC's reputation is.
NGC has a long-established reputation as the leading TPG (third party grading) service. They do no guarantee the authenticity of ancient coins, unlike world and US coins. Also, their grading scale system for strike and surface varies a lot in my view. They have made mistakes, though not too many, and I sometimes disagree about an authenticity decision, but on the whole they're trustworthy and reputable, if you want to slab an ancient coin or other coin.