Repairing weapons is key to making sure they have all the damage they can do. Also, your respective skills with the types of weapons you're using directly corresponds to this as well. While the game is presented like a first person shooter, it's first and foremost a role playing game in terms of what's going on behind the scenes in regards to combat. If your guns are repaired, and your skills are high for the weapon you're using, both your damage and accuracy will increase significantly.
If I might make a recommendation, I'd say to completely avoid doing any type of hand to hand or melee combat. Don't put points into either, and don't use those types of weapons. Stick to either small arms (pistols, submachine guns, assault rifles, sniper rifles), energy weapons, or big guns. Small arms is generally the best to invest in, as it's the type of weapon that's most prevalent in the game, especially early on. I ranked up my big guns skill a bit and used the weird gun you can make that shoots cans and garbage. It's actually really good early on and helps you save up ammo on your other weapons, but all the garbage you use as ammo counts as weight you're holding. As Elfa said, either rank up your own repair skill or frequently pay merchants to repair your weapons and armor quite regularly. Also, pick one or two guns you want to use regularly and buy tons of ammo for them. If you're still pretty early in to the game level wise, just wander around near Megaton and kill whatever is near there. If the flies are still causing you problems, you definitely don't want to be going places where Super Mutants are. You're just not ready for them in regards to your skills and equipment.