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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.
How on earth do you/would you deal with 3 of those zombie things using only melee? Do folks actually use the suits much? I have one and keep it safe in my lock up as I am too worried about losing it...