If you’re willing to grind skills a little by doing repetitive things, there are a few things you can do in/around the starting shelter that make a big difference.
Get a few levels in throwing: If you don’t have armor or levels in melee/dodge, you won’t last long if you try to just hit everything you see with a pipe. Grab a few rocks from outside, then go inside the shelter (preferably downstairs, where nothing will get you,) and throw them at a tile. Pick them up. Repeat. While this is boring and gamey, with a couple levels of throwing, a few rocks, and proper use of kiting and bushes, you can kill lone zombies without closing to melee range. This can make raiding your first couple houses easier.
Knife spears: If you use a rock and a nail to make a fishhook, then use “(” to deconstruct it, you can get your fabrication skill up to 1. If you the go into the woods and 'e’xamine bushes, it’s pretty easy to get your survival skill up to 1 as well. Once you’ve done that, you can use a long string, two-by-four, a spike (made of scrap metal), and a rag to make a knife spear. All of these things are available in the shelter. It’s an okay early melee weapon, but it really shines when you throw it. The problem is carrying more than one, which leads to…
Learn to sew: With survival at 1 and a pocket knife, you can make a wooden needle. If you disassemble some strings, (or rags, if you’re desperate,) you can get thread. By cutting up curtains, (or the clothes of the zombies you’ve killed,) you can get rags. You can then craft simple clothing items to get your tailoring skill up a few levels, cutting them back into rags after you make them. Also, reinforce the clothing that you want to keep by applying your wooden needle with thread. You’ll want to get your skill level up high enough to craft a trenchcoat and a backpack, (and maybe boots.) While it’s not body armor, if you wear a few layers of reinforced clothing you can take quite a few more hits before you go down.
Now, all of this grinding will take a day or two, so you will probably have to do at least one less-equipped excursion to get food and supplies. (Be cautious and stealthy. Consider doing it at night when it’s easier to get away.) However, if you do these things, by the end of the second or third day you can easily have a trenchcoat, hoodie, gloves, boots, hat, backpack, 3-4 levels in throwing, and 3-4 knife spears to throw. You’re still vulnerable with this loadout; mi-gos, hulks, and getting mobbed will still ruin your day. However, you should be able to handle a few zombies at a time without a scratch, which makes exploring the towns much, much less dangerous.
(Many people don’t like grinding to gain skills, which is understandable. However, if you’re just learning the game, grinding will help you survive until you figure out how to live without it.)