The difference between “I and my friends” and “my friends and I” is purely a matter of courtesy - they are both grammatically correct.
The latter though, is more common-place, considered more polite, and seems to flow better. In formal standard written English, subjects of verbs must be in subjective form, conjoined or not.
My friends and I. Mr Smith and I. My husband and I. The King and I. My friends and I are going on holiday to Bali. Mary and I are having dinner tonight.
Which is correct? My friends and I or my friends and me.
My friends and I - when it is the subject of the sentence. My friends and me - when it is the object.
My sister and I are going to meet David today. (as subject) David is going to meet my sister and me today. (as object) My parents took my brother and me to Bali every year when we were young.