Utility vest is free, and I'm usually not carrying enough stuff for it to be a huge deal. If I run, I'll keep it all on, since it only encumbers melee and if I'm in a situation where I have to run it's probably an emergency shotgun situation. If I decide to go killing, I'll drop the pack and all the loot I've picked up (notice that I don't need it to carry the stuff listed, meaning that even in the unlikely event I have to leave it behind I don't lose much of value), which drops encumbrance to just the kevlar.
Which, admittedly, is significant, but the penalty to melee is more than surpassed by the ability to almost completely ignore slashing damage where it hurts the most.
If I'm deciding to hunker down at a window to fight off a bunch of basic zombies, I'll drop the kevlar and the backpack both, but less so as my melee skill improves and it becomes less important.
Also, I should add that I also often carry a second backpack in my backpack, just in case I find something huge that I want to carry back to my base. But that sort of stuff really needs to be dropped before combat anyway - I can always come back for it later. Or, if its too hot, abandon it altogether, head a town over and get a couple more.
The key is not getting too attached to stuff.
edinsert: Also, about sight and such. Do the zombies attack as soon as you can see them, or are there any chances of getting by them unnoticed?
They do not notice you right away, no - I don't think your auto-stop triggers until they do, so that's a good sign. However, seeing you definitely increases the odds, which is why it's better to travel at night - they can't see in the dark either. (especially with night vision goggles, night travel is amazing)