Save often.
If you find something with a unique name hang onto it because it might be fun.
Find a safe place to store spare loot, Megaton House is my personal favourite.
Don't level up Barter because you will not need the skill.
Melee weapons pay off quick and are very fun to use, but energy weapons and small arms are just as fun and very useful in mid-late stages of the game.
Get Broken steel.
Don't kill people if they have a name, unless you have a very good reason.
If you get bored just pick a direction and start walking.
Level up repair a decent way, same for science Lock pick and Speech, how much is up to you.
Don't try to be a master of all weapons, its not going to work.
If you can't decide what loot to take with you try looking at in terms of caps-per-weight.
Get a sweet suit and a sweet hat.
Lincoln?s Repeater is a good weapon, if you find it keep it.
The animal friend perk is a must have, it's a life saver at low levels and fun at high levels.
Never level up a skill to 10, if you get broken steel never level up a skill to nine.
Some quests are a little broken, don't worry about it.
Some items can only be repaired to a worthwhile degree by Trade caravans, avoid their death at all costs.
If you disagree with anything I've said then ignore what I said, its your game.
Finally (I can't make this clear enough)
Save often and in more than one save slot. Fallout 3 has many glitches and the only way to ensure you are safe is to save regularly. Keep one save file at least an hour behind you (in terms of time spent playing), that way you will only lose an hour of playtime if something goes amiss in your other save files.
And remember: Better Dead than Red!