I keep thinking about this and I can't choose.
My idea is to use a blade (Eventually Chillrend) and frost magic, though I will especially just use my blade. This means that my character is much more focused on being a warrior instead of a mage.
Thing is, she is still able to use magic, and the companions probably dislike that.
I guess I could also join up at the moment where I only use a blade, and then my character discovers she/he (Not sure yet) can use frost magic after becoming Harbinger.

The Companions have no objections to magic, whatever works with killing beasts is A-OK.

I don't think this is correct, when you attack Vilkas with magic while sparring with him he tells you they don't do battle with magic and Kodlak said that magic and trickery is for cowards in his journal.

Anyway when i run a battlemage i forgo using magic when i'm with the companions, just think of it as training as a warrior with the companions and as a mage with the collage then putting the two together.

I suppose I could join up, trying to earn their respect without using too much magic, it would make me look like a show-off.

You can change that as Harbinger of the Companions, technically.

They don't care if you use magic or not.

I think the sparring thing is different, obviously you don't want to end up accidentally cooking someone to death with flames or something, and although Kodlak frowns upon it, it isn't outright banned.