Well, my personal way of playing is raising Small Guns first, Sneak second, Repair third and then lockpicking/science/medicine after.
When picking your SPECIALs, make sure you know how you're going to play BEFORE picking points on each. I tend to go for guns, so Agility is good for me, but I'm also a pack-rat so having extra strength to carry more loot is nice too. Intelligence is always a great one to go for as it gives more skill points per level up.
Word of advice, no matter what route you take... When you're doing the G.O.A.T., ALWAYS make sure you tag at least 1 weapon style. This will make things a little easier towards the beginning.
My general play-style is sort of a sniper/scout/thief. Pick up a rifle as soon as I can and pick off my enemies at a distance. The reason for Sneak, aside the obvious of not being detected, is that when you crouch and shoot the opponent, you get a Sneak Critical. A well aimed headshot will almost always decapitate the foe when you have a high damage weapon. Believe me when I say that picking every enemy from afar (and being able to switch to a pistol for closer combat) will make the game a LOT easier to bear.
Generally, I try to stick to useful pistols that are easy to repair (10mm being extremely common) for close combat, a base machine gun for groups (10mm sub-machinegun or better still the Chinese Assault Rifle) and a sniper rifle for longer distance. If you're having difficulty getting a Sniper Rifle, once you're pretty good with it, a hunting rifle works well too. All 3 of my choices become pretty commonplace later in the game. Raiders will have pistols, super mutants will have Chinese Assault Rifles (though the Assault Rifle is more common from them) and Hunting Rifles, Snipers become more accessable when higher in level in from merchants.
One last thing. Pick your perks WISELY. Don't feel that you HAVE to pick what I do, but I suggest not picking the ones that give a few extra points on skills and go for the more all-round usefulness ones like Scrounger (more bullets when you find them) or Child At Heart (special dialogs appear sometimes when talking to children).