Here is what I do:
Run a patch with barrel cleaner
Run brush about 20-30 strokes
Run clean patches till clean
Run one patch with a touch of oil

I load 5 rounds of each type of ammo.
Fire 3 shots
Take 5 minutes or more to cool
Fire 2-3 more

What changes do I need to make?
Should I thoroughly clean barrel after each differing type of round so they have the same baseline?

What are your goals? Since you're starting with a slightly oily bore (which I do) you need to fire a couple of fouling rounds.
If I am firing a series of cartridges where the only change is the powder weight, I will often fire two or three groups between cleaning. Sometimes more. When I change powders or bullets, I start with a clean bore.
I don't know that that's the best way but I try not to be too anal.