Well, ideally, I'd do my best to make my own set of armor, probably going for either chainmail or scale mail since it'd be lighter and more practical than plate yet still offer significant resistance against walker bites. I'd also carry a hatchet and maybe see if I could find a sword of some sort. I'd basically live as a post-outbreak medieval warrior or something.
Realistically, though, I'd attempt to get my family some place relatively safe, whether with a community or in a place that isn't high risk of being overrun. We'd do our best to work with others because really, in the world of TWD, numbers really are the best defense. The only issue is that people become just as dangerous as the walkers, so we'd exercise some major caution. My preference would be to end up somewhere like the Greene family farm and stick around there long-term, building up defenses as need be, maybe even creating a wall something along the lines of the Hilltop Colony.
After all, (SPOILER for anyone who hasn't read the comics or seen the show) the farm wouldn't have been overrun except by complete happenstance and bad timing and chances are, had Rick's group not burned down the barn and had they come back weeks later, most likely it would have been completely salvageable. Plus, somewhere like a nice, large farm gives enough land, resources and visibility that the only real long-term danger would come from humans and at least humans can sometimes be reasoned with.