I done my fair share of both, but threading is a bit more difficult. I use a battery powered drill for tapping, BUT it's easy to break the tap.
If you look up the proper sizes of drills for tapping, you'll find there may be more than one drill that works.
The difference is the % of threads, or gripping strength and for different materials. All this means is that the tap may go in with less effort than if a different (smaller) drill were used.
Here's a chart:
As far as getting the tap square to the surface, use a pre-drilled block of any appropriate material to guide the tap into the hole.
The hole in the block should be drilled on the drill press so get it square to the base of the block. Starting a tap in the D/P is difficult because the quill is spring loaded to stay UP, pulling it down while rotating it is not that easy. I rarely use this method.
You will get better with practice, and by checking from 3 o'clock and 6 o'clock to keep it square in all axis. Pretty soon you won't need the guide block.
There are 2 types of tap handles. The most difficult one in my opinion is the long fixed handle because any tip in either direction will cause the tap to be slanted, AND it is difficult to apply downward pressure to get the tap started:
The other type is a sliding "T" handle, easier to apply downward pressure AND often comes with a countersunk center on the top end to start it under a drill press: