The 'get-together' part is right, but the 'for 10 years' is ambiguous - it could mean that you are going to celebrate for 10 years! So I'd say 'to celebrate our 10-year acquaintance.'
Well if you just put 'for 10 years' at the end of the sentence, it's not clear whether it's 'acquaintance of 10 years' or 'celebrating for 10 years'. So to make it clear you have to move the '10 years', so to show it applies to the acquaintance, you make it an adjective. It's 2 words acting as 1 adjective, so you join it into 1 word with the hyphen ('-').
As I said above, 'acquaintance of 10 years' is not correct - '10-year acquaintance' is better.
However, you could use that sentence if the 'acquaintance' is a person. So if everyone's known Jeff for 10 years, and held a party for him, you could say 'We're having a party for our acquaintance of 10 years, Jeff.'
As for acquaintance vs friendship, it would entirely depend on the