5W/40 fully synthetic. It will give better cold starting, slightly better fuel economy (synthetics use less energy) and synthetics degrade less than traditional oils, so the engine is better protected.
Basically, none. You could buy a 5W/40 synthetic car motor oil as it will meet the same API and SAE specs for petrol engines and will probably be cheaper for a larger volume. Halfrauds usually have some sort of offer on synthetic oils. I worked in the oil industry for 25 years before being made redundant by Shell. The only oil you NEVER put in bike or car petrol engines is oil designed for diesel engines. It will cause bore polish and the compression and oil consumption will go through the roof. The only cure is to have the bores honed or rebored.
Be careful, you need to check the SAE and API ratings, as cheaper oils meet lower specifications. What you want is the highest alphabetical letter after the S and C on the label, e.g. SM/CH is the latest API rating (I think) and will be better than SJ/CF, which is an older obsolete spec.
Yes, I'd go fully synthetic all the way. Shell used to do a semi-synthetic bike oil called Gemini but I think that's been discontinued. Synthetics won't cause the 'black death' sludge that can form inside engines as they are more thermally stable.