Typically I would handle the setting, yes, but if you prefer to have more involvement and input, I'm totally open to ideas. I do however handle much, if not all of the plot. A bit of mystery, lack of spoilers and all that jazz.

You would make the hero (Or Heroes, if you prefer to have multiple hero characters throughout) and I would do anything else that you wouldn't want reign over. You could also create non-hero side characters, if you'd like to have more control over the interaction, but that would be up to you of course. Typically, they start off with your main character going about his/her day to day life, whether it's rough, solo, with friends, however you'd like it to start off. Within the first few chapters, you'll be greeted by a pretty blatant antagonizing force which I'll use to contrast your character completely depending on their personality. During this encounter, your character may find that he has innate powers that he can only access briefly, or if you'd prefer a less power-oriented growth curve, would gain access to abilities through other means later on. This first encounter always results in a crippling defeat, and often nets some brutal losses, or a bruised ego, depending on who you find yourself against. From there, your character would make his first major decision which dictates exactly how their path begins.

For example, one character might seek vengeance, and the power to enact that vengeance either through training himself, finding a mentor, looking for artifacts, etc.

Another character may be crippled by the defeat, and go through an arc to regain their confidence before they even decide to enter their primary 'origins arc' so to speak.

The options are limitless, and ultimately, up to you and how your character acts.

I like the post-apocalyptic idea, and I'm already brimming with scenarios! In a setting like this, where monsters and magic are dangers rather than accessible resources/allies, your character might either be well adapted to survival and danger before he gains access to any otherworldly abilities, or find themselves under the protective watch of another group/individual, perhaps an older sibling or parent, or a group of friends, something along those lines?