How to Vacuum Properly?

Very gently you want to lift very little of the substrate into the tube. The cloudiness is most likely due to ...sticking tube in sucking gravel up and then lifting the tube ...the gravel ,that is still dirty falls back to the bottom ..getting rinsed by your tank water .
The best way would be to stick the tube in and lift just enough substrate That it still tumbles in the tube ( rinsing ) when the water flows clear above that portion slowly lift the tube and move it to another section and repeat.
What size of substrate is it btw.....would help a bit.
On some of my tanks I just suck the substrate out with a 3/4 inch hose into a 5 gallon bucket that is placed in a larger tub when the bucket starts to over flow into the tub It is pumped into the drain.By the time thats done it just needs a quick rinse and back into the tank...I hate vacuuming

On this topic.. is it easier to clean gravel or sand?

IMO i think sand looks nicer especially the white sand.

Plan to get it but don't want to be vacuuming 5+ times a month,

Sand is easier to clean in a way because you can just sort of hover over it. The PITA factor is that it is all to easy to suck sand up if you stick the siphon too close to the sand. I do find that with sand, more crud winds up in the filter as opposed to falling in between pieces of gravel and staying there.