Having a few G of cash when you are level 1 is HUGE. It is critical to get good weapons and armor as soon as you can. A buff level 5 acts like a normal level 8 player - get the gear and upgrade your gear constantly. You may need to buy cheap aika gold from friends or send some over from another toon you have.
Also, if you Do not have a cash influx, you will waste a lot of time generating basic economy to upgrade spells – it is a serious time sink if your trying to power level. 1G minimum, preferably 10G or more to power you past level 20 quickly. The process of getting yourself uber gear or enchantments is called twinking and can work wonders (+100 health on chest and Fiery Weapon that hits for up to 200 damage per fight at level 25? nice).
Another power strategy - have an alt parked at the AH and use it to get equpiment for your power leveling toon (then use in-game mail, of course). This saves you the trouble of trekking back to the AH all the time and becomes very handy when your toon is not on the same contienent as the AH (starts to happen often around level 25).