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You'd be surprised with the right perks. Although I haven't got very far yet so this playthrough could be interesting. I think I'll spend a lot of time leveling up before I actually tackle the bulk of the main story.
By zombies do you mean the ghouls? They are OK if you find it difficult put on VATS and aim for their legs, most of the time you'll cripple them and laugh hilariously as they chase you around crawling.
I really enjoyed fallout 4.
Just try to focus on a few things not being a master of everything. Flying things are annoying but focus on vats or sneak. Sneaking will give you a 2x damage bonus.
Also always have a follower - they will 9 times out of 10 soak up the damage for you.
My first and only gameplay (just finished) was mainly around pistols and sniper rifles.
The playthrough I have just started I am aiming to be melee only so far I have a tire iron and a lot of balls charging into a big group. The first big hurdle will be trying to fight off a deathclaw. On second thoughts I might have to avoid them for a while.