Character history
You will, effectively, be playing two characters who share a body (perhaps more). Your initial characters will start off in a more or less typical D&D world in a more or less typical D&D situation. Before they reach 3rd level, things will change horribly. Your characters will undergo a mind-shattering experience, and will be merged with a human living in a world with very little in the way of magic (I'll be using a map of Europe c. 100 BC, and we'll be starting in Italy somewhere south of the Rubicon, let's say at the end of a nasty slave rebellion). Your second character can be a commoner, a slave, a professional soldier, or some kind of visiting foreigner, but nobles are Tieflings and Tieflings are nobles. After this change, your first character's personality can exist in any state you want, from a distinct second personality to a merged one. Something to decide on is how your character feels about these powers, and whether or not he or she wants to be rid of them. The default goal of the campaign will probably involve separating the two personalities at some stage. You can take a bonus (that makes sense in the context of your character's background) in line with the Forgotten Realms origins bonuses for having a reasonable character history.
Power source issues
What power source your character uses will be an important factor in role-playing. Someone with the martial power source will seem like a super-athlete to most commoners, with an uncanny sort of confidence and movement. Someone with the arcane power source will see the underlying threads of arcane power that permeate the world, and so give off a kind of crazy vibe in addition to a nimbus of magical energy (Warlocks have such a powerful nimbus that it grants them concealment when they move). Someone with the divine power source may have a halo or mandala. The primal power source might cause strange spiritual disturbances, or cause little elemental motes to float nearby. No matter what, it will be painfully obvious to any normal person that you are more than a normal human. Deciding exactly what manifests is up to you, but it should be interesting. You will normally get a penalty to interactions with normal people when your powers are on display, but you could get some kind of small bonus (like +2 to a skill or an extra class skill) if the display you describe is cool enough.
If you want to turn off your powers and appear to be normal, it requires you to take a feat and imbue some kind of short ritual or item with the power to suppress your tells. It could be something as intricate as a tattoo that binds your power if a single scratch is added to it, a holy symbol that denies you your power whenever it is covered, a cloak that hides your uncanny beauty, a poultice that masks your presence from common spirits, etc. If your idea is cool enough, I may tack a small bonus onto your suppression feat. Your second character will be entirely in control when you are suppressed.