In addition to the above, my tip is to take decent stats - high strength, at least 12, try for 14, dex at least 10, better 12. Decent perception - shoot for 10 if you can. I tend to not buy any skills, putting everything possible into stats. If I ever did take a skill, yeah Dodge would be the only one I'd sink a point on.
And throw stuff, it starts out weak but quickly gets to be pretty useful. Rocks are OK to start, but I get better damage with ceramic shards (smash toilets) or lumps of steel (if you can afford the 2-volume, probably because they're heavier. And those are easy to replace if you need to drop them to use the inventory space or because you needed to flee. It's really REALLY handy to put some damage on a zombie before he can attack you, it slows him down and lets you finish him off in a hit or 2. Or throw other tools/weapons that you are carrying, better to finish it off from a distance than risk a hit, especially before you get better armor. If he's still not finished off, lead him away, circle around and pick up your throwing stuff again, rinse and repeat. Just be careful throwing anything vital in case a spitter shows up.
My preferred early weapon is the cudgel - easy to make, reasonably fast, +2 bonus to hit, and has block, parry and rapid strike iirc. The knife spear is nice too - a bit more trouble to make, better damage but only has Block, which is still very helpful for survival early on.
And to reiterate - you MUST watch your encumbrance, and status effects like hunger/thirst or especially pain. Getting slowed down will make you way easier to kill. Run away, repair your armor, bandage up, let your pain go down, go into fights fresh and fast whenever you possibly can.