The diameter of the prop is to dissipate (i.e. transmit) the power - a more powerful engine needs more diameter. Or blades.
Pitch is to do with matching boat speed vs engine speed. You choose the pitch to match the max power RPM of the engine with your required speed, usually this is the hull speed where, rule of thumb:
(hull speed in knots) = 1.34 * sqrt(waterline length in feet)
In between the engine and the prop is usually a gear ratio, often 2:1
For more relaxed engine use often people overpower and under rev. I.e. if you have surplus power go for a higher pitch prop to reduce engine revs. A 6hp engine on a BC20 probably only requires 3hp actually generated so you run it at reduced RPM - bear that in mind when using this ready caclulator:
https://goodcalculators.com/boat-prop-calculator/I believe 10% slip is correct. If you get enough power for anticipated conditions at 3000 RPM (do you?) and the gearbox ratio is 2:1 then it's a 5.4 inch pitch you need for 6kts.