Press F1 while in game, has a list of shortcut keys that are very useful. I didn't know about it the first time I played through and wish I had.
A few tips...
Pay attention to what people say and the environment around you (you have a look option), sometimes there will be quest hints that are not very obvious at all, and it won't be written down in your PIPboy or anything. An early example is
Spoiler The girl in the first town mentions she was originally from Vault 15, and last she was there the elevator wasn't working. Though it's never really specifically stated, you will need to find a rope and use it on the shaft to climb down, something you have to figure out by yourself.
Stats are more important in the first games than in FO3. Having too low of stats can limit your actions or dialogue options in some cases. Most can be raised over the course of the game by at least 1 point, with strength being able to be raised a lot later on through armor, so unless you play a melee character you can leave it average. Agility and Intelligence are both important stats, mainly for action points and extra skill points. If you start with 10 agility you can get in two regular attacks with a standard gun per turn at early levels, though if you find a way to raise agility later it will be wasted. Perception helps to hit chance with guns I believe, so it's good to have fairly high if you plan on doing a lot of shooting in combat. Of course you can try for a pure pacifist (though in some cases you will have to run as combat isn't completely avoidable) or let party members do a lot of your fighting, really depends on the type of character you want to play.
Honestly, since stats are so important and having higher intelligence gives more skill points anyway, I find Gifted to be a very useful starting perk and probably more overpowered than any of the others. Good for a more well-rounded player for a first time go through also.
Skills wise, stealth is more powerful here than in FO3. If you really pump up stealth, and have good small guns skill (perception as well to hit long range), get a nice rifle and you can play a sniper and just kill people from the shadows pretty much. You can also avoid a lot of combat situations with stealth. Stealing is also pretty powerful, especially early on when you are poor. I like playing rogue-like characters in FO1 + 2.
Lockpick is pretty standard, you can use it to solve some quests plus get loot in 'dungeons', pretty much like in FO3.
Speech if you want to have the best non-violent ways of dealing with problems. Usually I find these give the most experience than other quest solving options.
Science and repair seem less useful early on, but later generally come in very handy when dealing with high tech equipment. You can get more information from a computer terminal when you look at or use it with good science.
Overall, explore and try to figure out different ways to solving quests. Save often, and keep a lot of different saves. Don't worry so much about the time limit in FO1, I used to freak out about it the first times I played, but I've never accidentally ran out of time. Just don't forget to keep looking for that water chip and asking questions everywhere you go.
Good luck!