My daughter has a Yamaha Raptor 50 ATV, and according to its manual, during the summer months, a 10w40 or 20w40 oil for most operational temperatures is the recommended viscosities. After break-in (she now has 25 hours on it), I have Maxima Maxum Ultra 5w40 in the crankcase.
I use this because one, I want a very stout oil in there, as in this model, the oil both lubricates the engine, plus does transmission pack duty. Two, since it is a full synthetic, the 5w factor means great flow and pumpability for the colder days. Now, if she decides to ride it this winter, I just might switch to the 0w30 grade of the Maxima, just to be on the safe side for the cold start.
One thing I have noticed about this engine is that it is very cold natured. It likes a nice long warm up before it will take off for her without stalling when she thumbs the throttle, so I know a thinner oil helps in that department as well.
Maxima Ultra is a 100% ester based synthetic. The Amsoil you mentioned is indeed a PAO based synthetic. I would not use the Mobil, not because it isn't a good product, I'm just one of those people that likes to boycott the major oil players and opts to support the smaller, specialized players in the lubrication field. Not that Amsoil is small at this juncture either, but they make IMHO a higher quality controlled product than Mobil does.
There are a few more specialty ones out there as well, such as Bel-Ray, Blendzall, PJ1, and Motorex, just to name a few. If you would like, do some searching to find out just the basics of each brand, then decide which one "feels" right for you.
Hope that this helps you out some. There are a thousand different lubricants out there, all gunning for your business and stating that they are, in fact, the best.