My current attempts to pay a pistol waving gun slinger. And thoughts all assuming VATS.
Three types of guns rifles (stock grip), pistols and automatics (automatic reciever); Pistols are half way between automatics and rifles, with more less accurate shots than a rifle and less more accurate shots than a automatic. The thing that makes pistols special is that they maximise the number of individually aimed shots; this allows excellent synergy with concentrated fire and Gnu Fu. So to use the gun-slinger perk you really want to max out Perception and Agility.
Also I decided that Intelligence was needed for Gun nut and science. If you are playing a general gun based character you can get away without this; just adapt to the best gun you have found so far. If you have committed perks to particular gun type you are more restricted, and will find being able to modify your weapons much more useful.
So Agility 9, Perception 9 and Intelligence 5 leaves two points left with the book. Your choice, I put one in Strength for armour mods but you could put them both in luck for criticals or whatever.
Again assume a gun-slinger, I decided I needed four types of pistols – heavy (sneak) short, heavy (sneak) long, light short and light long. Heavy guns to one shot ideally with a sneak bonus. Light guns to get as many shots off as possible while under attack. So building one gun for each ammo type this is how I set it up.
Heavy Long: .308 is the natural choice as they have the longest built in range. All even won't be as good as a sniper rifle but with gun-slinger bonuses that might well change. .308 has a slow firing rate, but that does not matter as your at range and can hop back into cover if you miss.
Light Long (Concentrated fire): .38 cheapest and (in my experience) the most common ammo does the least damage, so best used firing away when no immediate urgency. Taking out turrets from cover, or popping away at range with low chances for the initial bullets to hit.
Light Short (Gnu Fu): 10mm and .44 (Kellogs pistol!) Panic gun. Light but more powerful than .38. I use for getting as many shots off as possible at short range. You know that moment where your ambushed by a pack of ghouls and you have used up all your action points... well this is the answer. Just give each of them a few shots in the leg and save a few bullets for those still coming. The .44 is the best answer but has much more limited ammo availability so keep that for the super real emergencies (packs of super mutants rather than packs of ghouls!). In my current play-though I picked up a 10mm with crippling bonus power – perfect
Heavy Short: .45, fusion cell. I use this for short range sneak attacks. .45 more powerful than 38 and 10mm. Better rate of fire than .308 in case you miss!
As for armour, first priority Agility and Action points then stealth then perception. At least thats what I am going with. (e.g. Military Fatigues, Champion right arm and wastlanders chest piece),