She already has a lightning grenade, so I think it would be logical to only do the Fist of Havoc.
Also, is History optional, or can I explain it sometime during the RP? I'm having a hard time coming up with ideas for it as I don't know much about Destiny's setting, etc...
You can keep it as Fist of Havoc for now and advance it later-on when you think you know what you'd like to use. You don't have to make it something 'different' from the start.
As for history, it's purely optional. According to lore, most guardians don't know who or what they were in a past life. As for the setting, I'll give you a rough breakdown of it.
Shit is fucked. There's dead people with space magic (our characters). There's shitty aliens with questionable aim.
Now, on a more serious note.
The setting is 200 years after The Collapse (When the Golden Age of Humanity Ended via The Darkness (I didn't name it)). The Last City has been formed, with various 'settlements' scattered throughout Earth. With this in mind, after you character was revived by their Ghost, one of two things happened:
1. They immediately went to the Last City to join the Vanguard (The Collective of Guardians whose main goal is to fight against The Darkness and anyone/anything that would threaten humanity.) 2. Roamed the Earth/Joined a settlement until they eventually joined The Vanguard.
Either way, you can design a 'backstory' for your Guardian after they were revived, but before or after they joined the Vanguard.
Example:
Following scenario 1: [X] was assigned to the helping patrol the wall as a 'fresh' guardian. Being shown the ropes by a veteran, it wasn't long before a Fallen Ketch got a bit too close and the Vanguard engaged the enemy. With [X] on the frontline, they proved themselves as a true guardian as they stood shoulder to shoulder with their veteran mentor and drove back the Fallen menace, ensuring the City would remain safe.
Following scenario 2: [X] roamed the ruined city of Rio de Janeiro before coming across a small encampment of survivors. Knowing they wouldn't be able the reach the City, the survivors merely struggled and did their best to survive. Slowly becoming part of their 'society', [X] became a valued figure among them as their protector and guardian. Eventually, [X]'s ghost was able to make contact with The Vanguard and ships were sent to not only retrieve the survivors, but also the Guardian as well to bring them to the City.
You have quite a bit of leeway in terms of Guardian backstory that isn't really explored in game for obvious reasons.