Which flux type to use for SMD hobbyist (home-made) PCB?
If a flux is "no clean" it means it doesn't, under normal circumstances, conduct electricity. The exception is when the flux gets burned by too high a temperature and turns brown. At this point it can start to conduct due to carbon deposits.

Water soluble flux conducts and must be cleaned before use.

My personal choice is to never use water soluble flux and to clean flux off with isopropyl alcohol as a matter of course.

I have two fluxes - one in a pen form and one in a syringe. I find I use the syringe one more than the pen one these days.

Both are Rosin based.

As always the exact properties and handling / cleaning instructions can be found in the datasheet. 

Fluxes designed for metalwork, such as soldering pipes, is generally an acidic flux and must never be used on PCBs or it will corrode things horribly. Only ever use electronic-grade flux.