Some things I've learned playing a 'borg.
While you're not invulnerable, chances are pretty good that even out of the box, you're going to be very resistant to any damage coming your way. Don't be afraid to mix it up or slug it out. In fact, most personal weapons will barely scratch you unless the GM gets REALLY lucky with his rolls.
Not all cybernetics are created equal. I don't recommend Embedded Combat Coding, for example, as it takes two Strain and 50 grand. If you need an edge, buy it on your next advance. Expensive augmentations like the Nano-Repair System or Synthetic Organ Replacement should be bought with Upgrade Edges, while cheaper toys such as Targeting Eye, Bionic Strength Augmentation, or the Climbing Package can be purchased with credits.
Taking Beyond the Limit does saddle you with one of the Crazy's Hindrances, but you can always spend an advance to eliminate that.
You're strong, so toting a nice big gun is ALWAYS an option for you. While you can't carry a vehicular weapon, there's plenty of heavy personal weapons to pick from. There's also nothing that says you can't mount that big gun on a Built-In Ranged Weapon cybernetic.