1. Pick a gun type and stick with it... at least at first. I like rifles as you get in hits at distance and they also include shotguns. Shotguns pack a powerful punch in close quarters. You can pick up a shotgun and a .308 pipe sniper within the first couple of levels.
The guns I'm using with my level 17 character are:
Combat Shotgun (close)
Combat Rifle .45 cal (mid range)
Pipe Sniper .308 cal (long range)
I also keep a pimped out 10MM for small pests.

2. Perks. Select Rifleman (if using rifles). Gun Nut and Scrapper are also essential. Take a rank whenever available.

Sneak is your friend. A successful sneak hit gives 2x damage. You can get (or build) a .308 cal silenced pipe sniper for one shot distance kills at very low level. Plus the ninja perk gives enhanced damage multipliers on sneak kills. Taking out one or two (or more) enemies at range before a gunfight is a big advantage. Trust me.

Perks that enhance damage, criticals, action points or VATS should be carefully considered.

3. Weapon mods. This is where gun nut and scrapper come into play. Scrapper should be obvious. Scrapping junk and weapons yeilds rare parts you NEED to make the best mods.
Gun Nut. Make the gun as powerful as you can by making a powerful receiver. Do NOT make an automatic receiver, that will nullify your rifleman perk. Every time you rank up in Gun Nut try to make a more powerful receiver. Find or make full stocks. Do NOT make a grip. That makes it into a pistol.

My Combat Shotgun does 105 damage per shot and I still have more improvements to make. Your guns should be doing similar damage.