G6 is most likely a good choice. Glass is very subjective. The kit zoom (14-42) is a great place to start. Another option is the 14-140 zoom which would give you an all-in-one solution. At longer focal lengths you can easily get sort of shallow DOF (decent background separation but not extremely shallow DOF which is difficult to control). Spare some cash for an ND filter and circular polarizer as that will help to handle the sun and to shoot at open apertures..

Since you are starting out and seem to be into shooting sports I think you can benefit from having such a versatile lens as the 14-140. As your shooting progresses that zoom may start to feel limiting - but then you will be in a more likely position to know what you actually want for your shooting. Like I said at first, it´s highly individual and many things you might think you need you can do without. If you shoot all kinds of sports then a zoom is indeed a must have, but if you shoot the same type of sport (from the same distance in general) you will know after a while what focal lengths you want to shoot in.

The other option is you buy one wide angle lens and one telephoto lens and switch between those. (after a while you might want to change them as you may find one or the other or both slightly off in terms of focal length for what you would like to achieve). Though this would be a better beginners choice if you were into making shorts and such.