Before you start the game you need to make up your mind on how difficult do you want the game to be. If you don't feel like an expert in RPG games I would recommend playing on the normal difficulty setting. You'll still encounter a lot of difficult moments, but on the other hand your character will grow stronger without any major problems and without you having to worry about choosing correct stats and skills. If you think you're a hardcore RPG gamer choose one of the highest settings. Bear in mind, though - enemy units will inflict more injuries and your character will have to work even harder to eliminate his foes. You should also know that the amount of experience points received for each kill depends on the difficulty level, so theoretically you should advance even faster.
I would recommend that you finish the game at least twice (or three times if you're going for all achievements) and obviously each time you start a new game you should pick an entirely different character. I would recommend playing as a negotiator with high karma, speech skills and perks tied to new dialog options and with a dumb evil warrior who doesn't mind being hated by everyone else in the Capitol wasteland. Obviously these are only my suggestions and I'm sure that you'll find your own solutions.
This chart can tell you more about seven primary statistics and can provide assistance in finding out how many points should be spent on them.
ADVANTAGES OF SPENDING POINTS
Increased maximum carrying capacity (by 10kg for each invested point); inflicting bigger injuries during melee combat; additional growth of Small Guns (two skill points for each invested point)
Enemy units appear on personal radar much faster; additional growth of Energy weapons, Explosives and Lockpicking (two skill points for each invested point)
Increased resistance to poison and radiation; longer health bar (20 points for each invested point); additional growth of Big guns and Unarmed (two skill points for each invested point)
Friendlier NPC's and more interactions with them; additional growth of Barter and Speech (two skill points for each invested point)
More skill points to redistribute each time you advance to a higher level of experience (11 as a base value and 1 more for every invested point); additional growth of Medicine, Repair and Science (two skill points for each invested point)
More action points while using V.A.T.S. system during combat (2 additional action points for each invested point); additional growth of Small Guns and Sneaking (two skill points for each invested point)
Additional points to all skills (minimum - 1, maximum - 5); increased chances of inflicting critical hits to enemy units (1% more for every invested point)
This chart can tell you more about certain skills and about their usefulness on the battlefield.
ADVANTAGES OF SPENDING SKILL POINTS
Merchants sell and buy goods for better prices. I would recommend spending at least 20-30 points on this skill, even if you plan on finding supplying in the Capitol wasteland or by stealing stuff from other people.
Improved usage of big guns. I would recommend that you act similar to previous "Fallout" games and decide whether you want to spend points on Big guns or Energy weapons. You shouldn't look for compromise. There are a lot of useful weapons amongst big guns, including miniguns, rocket launchers and the fatman itself.
Improved usage of energy weapons. Like I've already said - you should decide whether you want to improve this skill or maybe Big guns. You can't specialize in both, unless you want to ignore other important skills. In my opinion this is a better category, because plasma rifles and Gatling lasers and among energy weapons.
Improves usage of explosives and better chances of successful grenade throws. Despite what you might think, this is a very useful skill, because you're going to want the grenades to land exactly where they were thrown. You should also know that by improving this skill you'll be given more time to disarm landmines.
Easier lockpicking. I would recommend that you stop building up this skill at 25, 50, 75 or 100 points, because these are levels of locks you'll encounter in the game. 50 points should be more than enough to open most stashes, however getting to valuable treasures will require you to expand this skill to the maximum.
Better effects when using medical supplies. This is an interesting proposition, because you'll be receiving more health points each time you use a stimpak. On the other hand, you shouldn't have any problems collecting a lot of stimpaks, so you can stop building up this skill once you've spent 20-30 points.
Improved usage of melee weapons. This is not a useful skill. Small guns are more interesting. There are a few good melee weapons in the game, however they will be used only to take down smaller creatures. The only advantage of spending points here is that you can use melee weapons as shields.
Better chances of performing successful repairs. I guess you may have a dilemma, because unless you'll decide to achieve 100 points here, the results are going to be worse than expected. You can ignore repair if you plan on changing weapons and armors often or if you don't mind the merchants repairing them for you.
Possibility of braking into more sophisiticated computer systems. This skill shouldn't be your priority, because even if you spend a small amount of points you'll still be able to hack into most systems. The only reason to put points into it will be to unlock cool perks for your character.
Improved usage of small guns. This is an extremely useful ability and you should keep investing points in it right from the start. The main reason is that a lot of powerful weapons are considered to be small guns. I'm talking about combat shotguns, hunting rifles and even sniper rifles.
Easier to stay in the shadows and improved chances of stealing. You probably won't be using this skill too often, because there aren't many opportunities to surprise enemy units. As for pickpocketing, you can spend a few points if you're frustrated by the fact that most steal attempts end in a failure.
Ability to convince others to your way of thinking by winning speech challenges. This is the most important skill for an intelligent character who resolves problems with a good response and not brute force. Even if you're not into talking to NPC's, you should still spend 10-20 points and you'll notice the difference.
Improved melee combat. Similar effects to Melee weapons only this time you aren't allowed to use any weapons. The only real exception are brass knuckles. You'll probably find a good unique knuckle during the course of the game, but nonetheless you should ignore this skill and spend points on something else.
It's very important that you make up your mind on how your character should look like before leaving Vault 101. You can still change almost everything (apart from quest decisions) while you're inside, including choosing new skill specializations and amount of points spent on each primary stat. Here's a list of hints on how you should build your character.
There are seven primary statistics to choose from and the value of each statistic can range on a scale from 1 to 10, however I would recommend avoiding extremely low and extremely high values. If you decide to give only 1-2 points to a statistic you'll probably be dealing with major side effects and the only exception is Luck, because you may decide to ignore it without having to worry about serious repercussions. Endurance may also seem like a less important statistic, but I would recommend spending at least 6-7 points on it. Otherwise you may have some serious problems trying to keep your main character alive. As for other primary statistics, it all depends on how you want to play your game. If you want to become a fierce warrior you should invest in Strength. If you want to rely on your speech skill and cunning you should invest in Charisma and Intelligence. Don't forget about Agility, especially if you plan to use the V.A.T.S. system often.
You shouldn't spend 10 points on any of the statistics, because there are Vault-Tec bobbleheads which will allow you to achieve the same effect and you can't have more points than 10. That's not all. Strength, Perception and Endurance may also receive additional points thanks to hidden perks and you can also consider choosing Intense training perk each time you advance to a higher level of experience. As a result 8 points seems like a safe value, especially if you're convinced on how you want to develop your character.
There are many difficult decisions to be made here. You can choose up to three specializations. Despite how you want to play the game Small guns should be amongst the three, because it's the most useful skill in the game, even if you're trying to avoid combat most of the time. As for two other specializations, if you want to become a bully you should invest in Energy weapons, Big guns or Explosives. A character relying on his intelligence should choose between Speech, Science and Lockpicking.
Each skill can achieve a maximum of 100 points and unlike the previous game you can't exceed it beyond 100. The situation here is similar to the primary skills - there is one Vault-Tec bobblehead for each skill and it can raise the skill by 10 points. You should also know that you can develop skills thanks to books and certain perks.