First-rate means excellent — the very best quality there is. 'A first-rate teacher', 'a first-rate meal', 'first-rate work'. It is warm, confident praise, and it comes with a small feeling of a judge stepping back and giving something its proper grade, because that is literally where it comes from: ships in the old British navy were sorted into rates, first rate down to sixth, by how big and powerful they were. First rate was the top class. The word kept that job long after the ships went. There is a matching family — second-rate and third-rate — and here is the interesting bit: those two are much more common today, and both are insults. 'A second-rate hotel' means not good, and 'third-rate' is close to rubbish. So the set is lopsided: one strong compliment, two sharp complaints. As for feel, 'first-rate' sounds a little old-fashioned and a little British to younger ears. It is safe and polite in writing — a reference letter, a review, a formal thank-you. Among friends, people are more likely to say 'brilliant', 'amazing', or 'really good'. Nothing is wrong with 'first-rate'; it just wears a jacket.