colin got the gist of it, fine is still a common term in european or british colonies(not the money you have to pay for redemption), probably less likely to be used in the states and younger generations
very fine looking is an exaggeration or imitation pun/ humerus way to praise beauty. as back in the 17~18th century literature and probably nobility languages, to be conservative, they would express things as "fine" or "very fine" which means without problem. modern usage is either a pun where one imitates how upper class spoke or simply when one could not find words to describe.
看起来不错 doesn't apply here since the "very" is used to emphasize the "fine" so it is better to translate as 很漂亮 or 無垢/無暇
note how it's very fine looking, it could also be used as very fine women or very fine men which is more commonly used when describing good people.
a fine-looking "noun" or perhaps a fine-looking "item" is a commonly used phrase. therefore a fine-looking woman not an appropriate usage as it relates women as commodities, it is usually seen in contemporary literature or medieval acts by plebeians or bandits when they use improper English. seriously you'll sound like some 18th century ragged bandit about to nitpick or molest some poor maiden in the streets