The following two sentences seem to have the same general meaning to me:
If I ever became a musician, I would grow my hair
If I ever become a musician, I will grow my hair
I was wondering whether one was more correct than the other.
Books for foreign learners of English describe sentences like If I ever become a musician, I will grow my hair as the First Conditional and sentences like If I ever became a musician, I would grow my hair as the Second Conditional. The First Conditional predicts a likely event if the condition introduced by if is fulfilled. In the Second Conditional the situation introduced by if is a more remote possibility, one that is unreal, unlikely or untrue.
As long as your verbs agree then they both are technically correct. There may be some linguist psycho-babble about which is which, but they are both mechanically sound.
However, it wouldn't be a bad idea to carefully review the connotations attached to your message.
If I ever become...I will tends to tip towards possibility and away from hypothetical speculation
If I ever became...I would sounds more hypothetical.
I suppose you could say one says maybe someday, the other says if it was possible
I'm probably wrong here, but to me:
If I ever become - is future conditional. Something that might happen in future. If I ever became - would be past conditional. If I had have done it in the past.
But in any case, as Rant says, the verb tenses need to agree. So if I ever became, needs to take I would, or I would have....
Both are indeed common and correct. The first is the past tense (AKA preterite) and the second the present. Note that tense is not always about time. The past tense can be seen as a remote option with respect to time, factuality/probability, and social distance. In this case, the use of the past tense suggests the speaker sees becoming a musician as a remote possibility.
As others have said, both versions are perfectly acceptable. But I don't think they're always equivalent.
If I ever became...
only weakly implies the possibility coming to pass, with no particular suggestion that the speaker either wants or expects it to.
If I ever become...
more strongly suggests that the speaker actually wants to become [whatever], and is perhaps making efforts in that direction, but is unsure whether he will achieve his goal.