Some very good products you've got there.
However, I am a bit confused as to why you have bought a few of them. Here's my thoughts....
Prep...Lime Prime is a hybrid pre-wax cleaner. some light abrasives in it, lots of fillers and a glaze all in one.
Glaze...Blackhole does the same job as the Lime prime...but not as good for cleaning.
Applying Blackhole after Lime Prime defeats the objective as the abrasives on Blackhole would rip off the lime prime beneath it.
Sealant....sealants are best applied to thoroughly clean paintwork. If there are glazes beneath them, this may lead to product compatability issues and the sealant failing. If Blackhole was used as the glaze, then poorboys Ex-P sealant is best used (chemically engineered to work together).
Wax...... putting wax on manually is usually faster and more accurate than by machine application.
There is one aspect you may wish to consider...... as you now have a machine polisher, why not take the opportunity to machine compound/polish the paintwork?