I'd get myself a meat tenderizer as my first weapon as it'd be real good to bash a zombies head in, I don't need to be precise like a hammer and I don't need to use an excessive amount of force either. After I've gotten that I'd of course try to avoid getting torn to pieces while collecting supplies from nearby houses and move closer to the city, I'd go to an area that is isolated and has open ground locked in with a fence so that I could take it over and call it my new home. Along the way I'd get myself a nail gun and stock up on a lot of ammo for it. See a nail gun doesn't need brute force to kill an enemy, nor do I need to worry about where to find ammo for it as any hardware store will have copious amounts of it and it's quite easy to kill zombies with. Just move in relatively close, Thwck! And the zombie's down.
Now after I've cleared out said area I would try to get others to move in there as well, I'd have to take the chance with survivors as there is strength in numbers and all I can do is put blind faith in them. Once we're all settled in we would reinforce the fences around the area and stock up on supplies, going out on runs every couple of days to bring back loot. But the most important thing is to get irrigation and agriculture going as fast as possible as food will go bad quickly.
Then we farm a little, maybe set up some sort of wind-power so we can get electricity, we go out on runs every once in a while and every day someone has the duty to walk along the fence and kill the zombies leaning against it. Eventually, when winter comes, the town is ours. See zombies already suffer from rigor mortis so when the cold comes in do you think they will be smart enough to get dressed? And hell, a swedish winter can get absurdly cold. So when the zombies have frozen down we'll simply walk around the town and smash as many heads in as we can. Hopefully we can set up a new barricade around a larger portion of the city so that come summer, we have more room to walk about.
That's the jist of it basically. As to whether or not we can survive 20 years that depends on raiders, cannibals, marauders, internal conflicts and deception about bites.
Another thing I'd do is wear leather. You ever tried to bite leather? It's real tough, so while the squeeze from a zombie bite might be painful it ain't gonna pierce through the leather which allows me further safety. Leather jacket, leather jeans (Although they will chafe(?) like crazy...), leather gloves; The whole deal. Only open part of my body would be my neck and head.
So yeah, just keep pushing through the summer until winter comes and then do as much work as possible to reclaim the city.
Alternatively I'd become a zombie exterminator (as cheesy as it sounds...), sure I'd need to learn how to properly defend myself and get a lot more fit, but the way I see it the longer it takes for us to purge the undead the longer they will stick around, and for every zombie we kill a living being might survive.