Cardio + strength?

Not if you're used to that much exercise. I wouldn't start from nothing to that...spin/cycling classes tend to work your legs more than your arms, so I'd say lifting arms/upper body after a spin class would be ok.
You can split it up into morning/evening to give your body more time for recovery as well (I often do yoga first this in the morning, lift on my lunch hour and then do cardio after work.)