You have a lot more to select than handlers, but at least your backstory is almost entirely irrelevant. It is worth figuring out what led to your hospitalisation, but don't worry so much about the what led to *that*. The reason for this is that it will influence your augments. Everyone gets a baseline muscular upgrade across the body, but whether you have a complete facial reconstruction, full cybernetic limbs, etc., varies. Keep in mind that, usually, you were already going to die before you were chosen. It's rare for someone with a decent chance of recovery to be on the list. "Blood loss" and "head trauma" are pretty easy excuses for that.
You'll also need to pick your preferred weapon - a single gun, not a class like handlers. Cyborgs are specialised, this training is brainwashed into you.
Of great importance is your conditioning level. You can pick from level 1 to 5, or minimum, low, moderate, high, maximum. The higher the value, the more devoted to your handler you are, and the less personality you have outside of that. This will be reflected mechanically, so choose carefully. As it is somewhat a sensitive topic, you absolutely should talk this out with your partner before deciding. Canonically, the decision is the handler's, but both players should be comfortable with the choice.