my rule of thumb for split timing: i'll start about 2 weeks before the swarm season in my area. So for me that'd be splitting early May for a swarm season that usually starts around mid-May. That what feels safe to me but some may recommand even earlier. Check with other beekeepers around you when swarming season starts or when they split.
As for using 2 bodies vs a nuc box, if you take only 2-3 frames from original, i would not give the split too much room to manage; let them grow in an adequate space for a little while and then jump to hive body. If you split equal then you may place both half in a body. Here with 2 deeps, i split half, give each one deep, making sure there's what they need to raise a new queen or introduce a new one in the queenless half.