Adjectival use will require a hyphen (first-rate ship) but when used as a noun (first rate), it does not. ... "First rate" is the name of a type of ship, like "frigate" or "destroyer". It is not a proper noun, and therefore it ought not to be capitalised.

Should First Class be hyphenated?

It is a compound adjective and needs to be hyphenated. I personally would have written it in exactly the same way. Hyphenation helps distinguish between possible variations like 'first class-passenger' that would have a completely different meaning (if 'class-passenger' could mean anything at all, of course).

What is a first rate person?

If you say that something or someone is first-rate, you mean that they are extremely good and of the highest quality. [approval] People who used his service knew they were dealing with a first-rate professional. Synonyms: excellent, outstanding, first class, exceptional More Synonyms of first-rate.