the dashing swashbuckler in me envisions myself as being a lone-ranger style survivor, I'd probably gather whatever supplies I need, find an isolated little shelter and call it my home until some scrappy-companion sneaks into my abode one day. I'd whip some big rifle or revolver and go
"what're you for lookin' boy" and it would be the start of an epic 80s era Post-Apocalyptic trilogy
the rational, calculating businessman I hope to be would simply stay where I am now, probably gather whatever friends were willing to stick around with me, and I'd try to establish some kind of community. I'd re-purpose my home, and the homes of my neighbors (assuming they're all dead and the homes are abandoned) as storage/living shelters or barriers to keep unwanted people/creatures/natural disasters from getting in. the community would have to be a marshal law environment with everyone carrying a gun and almost any infraction being punishable by banishment. I would not allow execution or killing as a form of punishment because humanity would be hanging by a thread as it is. Even if said criminal failed my community they could potential create a new life out there somewhere. The society would probably communist in nature with no real private property. Everyone, including myself, would sleep in the same type of shelter and we'd all eat the same kind of food. Alcoholic consumption would be banned as the alcohol could be used for medicinal purposes. Any kind of medicines or anti-biotics would be heavily guarded by an ever shifting group of guards, and would only be used in extreme emergencies. Everyday a small band of people would be sent beyond the barriers to forage for supplies. I would keep a consistent list of "community goals" that would always be worked towards. (the first being to clear away rubble or unwanted buildings, second would be to establish some kind of agriculture etc.)
the realist in me figures I'd probably be dun-ded