Looks good, just remember that if your already pushing yourself with cardio atm and your not lifting, once you start lifting you will have to lower your cardio intensity a bit, consider the 20mins cardio before lifting just a warmup to get the blood flowing, I over did cardio once and its not fun, couldnt do anything for 2 weeks cause of a headache.
I think the best routine would be HST and I have also heard DC training is good too for size but I heard its only for experienced lifters and its a bit more brutal, I doubt it would be best for a cut. Lots of people have had great results with HST on a cut so you might wanna go with that.