Opening "best of minors"
Your opening style seems fine, but responder should prefer to bid 1 heart or 1 spade holding four cards in the major to go along with support in your minor. That is, after you have opened 1C, partner should respond 1H holding

x
xxxx
xxx
AKxxx


There are a number of reasons for this; perhaps the most important is that making ten tricks in a major-suit contract is almost always easier than make 11 tricks in a minor-suit contract when you have a 4-4 fit in the major and a 5-4 fit in the minor.