Well, it depends on what kind of character you are playing. But as it's your first time, I really suggest to invest those points to Small Guns -skill, as you don't have any bigger guns yet and unarmed/melee weapons may be a bit too difficult in a long run.
When you find bigger guns (miniguns, rocket launchers and such) you can decide if you want to put some points to Big Guns -skill as well. Same goes with energy weapons (all ranged weapons which use Small Batteries and Micro Fusion Cells as ammo). My suggestion is that you spend points to Small Guns, and later decide whether you go for Big Guns or Energy Weapons.
Rising fighting skills (guns, melee, unarmed etc.) rises your change to hit the target. I don't know the specific calculation, but basically it's skill minus all the variables that affect the chance of hit (light, distance etc.) For aimed shots there is also variable which describes the difficulty of hitting that certain part of body. Also, other skills also affect to the game the same way. Your chance of success is your skill minus all the variables affecting the possibility.
As the game is totally completable with fighting skills alone, I suggest that you play the game by concentrating on fighting skills, and after that replay the game at least once to try on different kind of things as you have better understanding on how the world actually works. Almost everything can be achieved couple of different ways, and some things are only possible by right character development (Abilities and skills).
BTW, what stats does your character have, and what skills have you tagged at the character creation?
Oh, and don't hesitate to ask, I'm more than happy to help you to get inside the beautiful world of Fallout (1 & 2).
