Every time you win a battle you get VR points(you start with 1500) and every time you lose you lose VR points. You get ranked according to the amount of points you have. The chances that you get an invitation for the VGC's rises the more often you get ranked in the top 100 in a couple of competition, so you usually don't get picked after you have been ranked in the top 100 once. So I would say it is better to battle a lot and lose/gain points then to battle and win a few times. But you should give it your best shot because some of the trainers out there are really powerful.
Conclusion: To get chosen you must be ranked high in countable competitions. After this you will usually get chosen for the VGC's
Hope I helped and good luck