1.75mm
Pros:
Requires less torque, so works with a direct drive (gearless) extruder.
Requires more steps/cubic mm of extrusion, so produces more precise extrusion.
Cons:
Costs more (by volume) than 3mm filament.
With a bowden extruder, print quality is compromised because the filament is springier.
Personally, I use 3mm filament, and see no reason to pay the extra cost for 1.75mm filament.
.2 nozzle
Pros:
Extrudes a finer line, making more precise prints.
Cons:
Extrudes a finer line, making prints take considerably longer.
Requires a higher torque extruder motor.
Clogs easily.
I'd start with a .5 nozzle, and switch to a smaller diameter when you find that .5 is limiting you.
For U.S. hotend suppliers, I suggest MakerGear.com and hotends.com.
In Europe, it's hard to beat arcol.hu.