Character creation: Intelligence is the most important stat. Strength and charisma can be reduced to 3 or 4.
Get the medicine bobblehead before you leave the vault.
Don't read any skill books until you get the perk that gives you two skill points per book.
Sell extra drugs. You don't need more than 5 psycho, rad x, buffout or jet at any one time. Sell extra components in the early game (sensor modules and fission batterys are good to sell). They are useless until you find schematics. That should bring in pleanty of extra coin.
Hoard stimpacks and ammo. Be sure to get the ammo scrounger perk - probably the best perk in the game.
Pick one style of weapon and stick with it. The easiest is small guns. They are plentiful and have the most ammo. Late game you will find more ammo for energy weapons and big guns. Also, while you can focus on lockpick and science, you really only need one or the other.
Repair weapons and armor before you sell them. A 60% repaired gun is worth more than 2 30% guns. Also, find a wasteland trader outfit (+10 barter) and put it on before you buy and sell anything.