The trick to versatile characters is threefold:
One, make liberal use of the many Attribute, skill, and dice pool modifiers out there. This is a world of dystopian transhumanism - you can become superhuman by selling bits and pieces of your humanity, or you can be someone gifted with otherworldly power - and alternately feared and envied by mundane metahumanity. The rules reflect this reality, which is why augmentations and adept powers give you such cheap power boosts.
Two, don't spread yourself too thin, to the point of uselessness. This varies from skill to skill. Combat skills require the most dice for consistent success, since you will be making opposed tests with negative modifiers. But it is best to stop at a point where you are still good at what you do, and not spread out until you can do everything, but do it poorly.
Three, look for useful synergies. For example, if you are playing a speed sammie, with high Intuition and augmented Reaction, then the Stealth skill group would probably be a good buy for you, even at a comparatively low rating. Likewise, a shaman who has a high Charisma can become a secondary face with just a bit of tweaking. Also do this from a more organic, character background point of view. Why does this character have all of these skills? What does he use them for? For example - he is a private investigator who works under the table - that would explain pistols, unarmed combat, the influence group, perception, data search, first aid, and pilot ground vehicle, among other skills.