If you can afford it, there are nice steel shingles that look like tabbed asphalt shingles. (We did not opt for them because they cost more than double when we looked into it about 15 years ago -- but now we wish we had coughed up the money at that time. Maybe the price is more comparable now - with more manufactures making steel tab style.)
We removed all old asphalt shingles prior to installing roofing steel on our outbuildings. One website says steel can be installed over asphalt... but when I think about curled-up asphalt shingles I have seen on old decaying buildings - it would make me want to remove the asphalt before installing steel.