This is a guide intended to make your stay in the wasteland as pleasant as possible. Fallout is a heavily character-oriented game, so from the very beginning the decisions you make will affect heavily how well you fare and how much you enjoy the experience.
 Make your own character
Though the game gives you the option to pick from a pre-made character with a brief backstory (Max, Natalia, or Albert), it's advised not to do this, as much of the enjoyment from the game is had from putting you in its universe.
 Character Creation Tips
As previously alluded to, the decisions you make here with stats will greatly affect your experience in the game. Players will find their playing style likely varies from any given other player, so it's important to pick carefully what attributes you want emphasized, and which are less important to you. Every point counts!
Does the obvious (damage), but also relates to how much you can carry in your pack. Characters big on item use will want to have at least a pretty high level of strength, especially those that don't use the Doctor or First Aid skills (more on that later). This stat will also allow you to use bigger weapons.
Mainly affects ranged weapons distances, but also the details you notice in the world, displayed to you in the information window. If you prefer to play unarmed (using knuckle and fist weapons, or no weapons), you will want to keep this to a minimum and spend your points elsewhere.
Determines your hit points, the amount of damage you take (and can take without dying), and your resistances to poison and radiation. At least a 5 is recommended for all characters.
Affects your conversations with people, including when trading (meaning better deals). As with strength, if you think you will be relying on items a lot (which most should), a decent charisma stat is important. If you wish to have a (mostly) non-violent character, charisma can come in very handy, as you can avoid conflicts and/or resolve them without resorting to fighting. It will also help you bag a few ladies (or dudes, depending on your preference).
Arguably the most important skill unto itself. It affects how many skill points you earn each level, thereby potentially affecting all of your abilities. It also affects your options in conversation. While it can be fun to play a 1 intelligence character and basically drool your way through the game, it's not really recommended, at least not for your first playthrough.
Affects a few combat related statistics, including sequence, meaning how soon you attack before (or after) enemies. For some this last one may be important, but note having this low brings two advantages: more points to spend on other things, and attacking last means you can heal for maximum HP.
The most mysterious attribute. It affects "how the universe views you", as well as random encounters, and gambling.
 Skills to consider and avoid
First thing is first: avoid the Doctor and First Aid skills like the plague (ironically). They are practically useless, especially when compared to the power and quickness of stimpaks, which can be bought in heaps, and for cheap if your strength, charisma, and barter abilities are all decent enough. Even when maxed out, they heal about 5 HP at most, and take up in-game time to work (which may or may not bother you). And you can't use them in battle. Stick to stimpaks and super stimpaks and you will have a much more enjoyable experience.
The second thing to note is many skills can be brought to about 100% (max being 200%) with books (very cheap with a high barter skill), and as such, are recommended to be avoided leveling up yourself unless you really want to specialize and max them out. Those skills are: Science, First Aid, Small Guns, Outdoorsman, and Repair.
Assuming you like to use 'em, small guns is generally an important skill, as these are prominent throughout the game. Big guns and energy guns skills bring their own advantages and disadvantages.
Great if you prefer to go at it bare knuckle (or with brass or spiked knuckles, or the great Power Fist).
Useful if you prefer to avoid conflict.
Good to have at a decent level, so as to gain access to good items, weapons, armor, etc., and goes well with Sneak and Steal if you like to go the thief route.
Goes well with Sneak, as you can 'reverse pickpocket' explosives, planting them on enemies. Combine this with a high agility, and you've made yourself one annoying opponent.
Useful for computer hacking and the like, while Repair is good for...repairing things.
Like charisma, it is useful for dialogue options and avoiding conflict.
Good for getting cheap prices on items from traders or vendors. Note that maxing out your Barter skill can be dangerous, as you may end up ripping yourself off in deals when you find out you have way too much stuff to trade and too little to ask for in exchange, which may bring on the problem of difficulty in acquiring new items and having to throw stuff away you'd rather not. Approximately a 150 skill rate is advised.
Affects your abilities at the casino in Junktown, while Outdoorsman, in tandem with Luck, determines your rate of bad random encounters vs. special encounters.