Since I give each cleaner its own applicator, cross contamination is not a concern.
Premier - Here I'm probably guilty of flagrant indulgence. I hold the nylon brush that comes with the PRC-3 kit against the record at a right angle to the grooves and spray Premier across it from outer to inner groove as the record turns. Some folks advocate spraying it on a cotton ball then applying as the motor spins the record.
Otherwise, all cleaning fluid gets applied with the motor off.
Bugtessel gets applied using the sprayer. I then ensure complete coverage with a foam painters brush, spreading it around by following the grooves. The only thing I use that brush for.
RRL wash gets transferred from its large bottle to a smaller drip bottle dedicated for it. I squirt some on the record then spread it with a likewise dedicated Record Doctor brush.
Congrats on getting a Loricraft - it is an excellent machine and your records will love you for it. :-)
Tim