I have over 300 hours on Fallout 3 and lots of good advice:
1. Get Broken Steel, and have it running during your game. It will enhance your experience a lot (raised level cap, new ending etc)
2. Most important skills for a well rounded character on first playthrough:
Small Guns
Lockpick
Repair
Take 'Comprehension' perk as soon as you can. It's invaluable as it lets you double skill points from books. Save any books until after you have this perk.
A lot of people are saying Science, but it is very rare to find a situation where Lockpick won't do the job instead. Unless you like hacking useless turrets, avoid Science until you have spare points, maybe as a fifth or sixth priority.
3. Pick up and repair every enemy weapon you find and sell it. Same goes for armour and bits and pieces. You will need to do a little grinding and selling cheap stuff in your first few hours.
4. When you have around 700 caps, go to Canterbury Commons (google for location) and speak with Uncle Roe. Invest in the trader named Lucky Harith. You will now always have a fresh supply of almost any weapon you need, including the all important Chinese Assault Rifles.
You can find Harith at Megaton, Arefu, Paradise Falls, Agatha's House, Rivet City or Canterbury Commons roundabout... just wait in two hour gaps until he spawns. Crow is also worth investing in.
5. Put at least 8 points into Intelligence, even 9. This will give you more skill points to spend each level. I usually sacrifice Charisma as it's pretty useless.
Agility is also very important if you're going for small guns.
6. Get out there and explore.... most of the fun to be had in F3 is discovering things for yourself.
7. Save all the time. Have at least 7 or 8 different save files in case of bugs, wrong choices or crashes.