You can pick up a mask that makes them completely ignore you anyway. You'll never have to fight them (except to get the mask) if you don't want to.
Anyway, since you've already seemed to solve your own problem (I'm assuming your quote "but I'm pretty sure I can stomach whatever the game throws at me" means the "zombies" don't bother you that much), I'll move onto your main question.
It's a lot of running around and exploring things. There are very few quests compared to other Bethesda games. You're meant to look around and find stuff for yourself. There's tons of areas that aren't related to any quests and you'll never find them if you don't explore.
I played through a surprising amount of the game with just basic combat armor, a hunting rifle for long range attacks and combat shotgun for close range, so you don't need awesome equipment to survive (although a plasma rifle never hurts, but people won't drop them until later in the game). There's lots of towns that are particularly fun to wander around in. There's a drive in, there's a ball park, there's a diner filled with bloody corpses and land mines, there's an elementary school where some raiders were trying to tunnel into your vault, there's all kinds of safes and stashes hidden inside of collapsing buildings, a crashed UFO, a missile silo that lets you launch an ICBM (although it malfunctions and doesn't launch), a satellite uplink station where you can call in a real nuclear strike on a random field (could be quest related, I never got the quest though) and you won't find any of it if you don't look.
Poll