So tell me, please, what are some tips I can use to keep one of these sorry suckers alive now that I can't even go to the place where the goodies are without getting mobbed?
Make sure your game is set to static spawn. This lets you clear a safe zone bit by bit as you move into a city.
When you start the game, check the shelter basement for supplies. Go outside and grab a rock, then come back to the shelter and 's'mash up some furniture until you have a 2X4 and some nails. Craft those into a Nail Board for a starting weapon.
Next, head to the most isolated house you can see on the map. Approach slowly, and only close enough to lure zombies out one at a time. Once one or two zombies follow you, retreat away from town and try to move so they have to cross a bush to get to you. Stand just on the other side of the bush, and when they step on the bush tile, attack! They'll be slowed down enough that you get free swings in, and eventually you'll be killing them before the touch you. Windows and car chassis work the same way inside a town. Repeat this until the house appears clear. Smash the window farthest from town and wait to see if you attracted any attention. If yes, keep dragging the zombies out of town and killing them. Don't forget to 'B'utcher the corpses so they can't rise again. If no, you have a relatively safe house.
Now you have 2 goals: Food/water, and armor. Every house has a kitchen with a refrigerator, check those, and the stoves for a pot/pan to boil water in. Once you have armor and storage (see below) you should be fine for the first day after a house or two.
For armor, you need to find a sewing kit in one of the houses, and a few items of
undamaged clothing in a house. Grab the string from the window you broke and 'D'isassemble it into thread to reload your sewing kit. Cut up damaged zombie clothes and sheets to get rags for tailoring work, and practice sewing by using your sewing kit on an undamaged clothing article (make sure it's something you don't want to keep, there's still a chance of destroying the item while practicing). You should get tailoring up to 2 or 3 pretty quickly, which lets you fit most of the clothing you find to lower its encumbrance, as well as make some new armor and reinforce it to keep you safer. My early goal is usually something like this:
Boots, socks, cargo shorts, cargo pants, a hoodie or (preferably) trenchcoat, glove liners, light or fingerless gloves, bandana and/or filter mask, safety glasses, some kind of helmet, and 1 or 2 storage items like tool belts, messenger bags, pouches, or a backpack. You can reinforce most of those items by using a sewing kit and rags on them, which makes them last longer in a fight and protects you from some bite wounds.
If you want to make sure you have a sewing kit, you can take the tailor profession at character creation, though I don't think it's really worth the points.
Once you have a clear house, some food, water, and sturdy reinforced clothes you should be in pretty good shape to continue slowly clearing the town and looting more houses and stores.