Fast EXP

From lvls 1-30 you should cut normal trees and burn them into fires. You should only have your hatchet and tinderbox in your inventory. Weild the axe so that only the tinderbox is in inventory, enabling you to hold the maximum number of logs possible which you can burn later. Once you are level thirty woodcutting, and level 35 firemaking, start cutting oaks with a mith axe. Do this till your about level 50. After this, get a rune axe (which you can weild at level 40 woodcutting) and cut willow trees till lvl 80. If you want to burn your logs, continue to burn every log you cut, otherwise you can either: drop the logs you cut; bank them at any local bank to sell later on for money or sell them any nearby general shop. Once you hit level 80 woodcutting and firemaking, begin the same process, but this time, cut yew trees to reach level 99. When cutting yews however, I recommend you keep them, as you can sell them for up to 300gp each per log.

 Woodcutting Prices

Bronze Axe:1gp
*Iron Axe:50gp
*Steel Axe:50-150gp
*Black Axe:500gp
Mith axe:1k
Addy axe:2-3k
Rune Axe:15k-25k

*rough estimate. 

 Firemaking Prices

Tinderbox:1gp 

 Logs

Normal:10gp ea
Oak:15-20gp ea
Willow:10-40gp ea
Maple:100gp ea
Yews:250-300gp ea
Magic:1k ea

Places to cut

Normal trees: Anywhere.
Oak: A few trees at Draynor Manor, west of Varrock and some south near the general shop at lumbridge.
Willow: Draynor Manor, next to bank. Also, for firemakers, better places: West of Rimmington and Port Sarim.
Maple: Camelot and on the pathway leading from Sinclair's mansion to the Fremennik Province.
Yews: Two trees just outside falador for woodcutters. Also for woodcutters, a more popular place is edgeville, where there are two trees. For firemakers, three trees can be found North of varrock Palace and 3-4 trees South of melzars maze. There are also four yew trees in lumbridge swamp, but these are infested with bots.
Magic: Some near the alter at camelot, and two trees located near the mage training arena.


Notes

My advice is that once you can use rune, try and get a rune axe as quick as possible. Dont get carried away in trying to cut 10k yews. Keep your goals small and achievable and you will reap the rewards. In my experiance too, willow is the best for players who want fast woodcutting and firemaking experiance between levels 60 and 80. But there are many different strategies you can take. Remember that most people will only buy up to 5k of yew logs during gameplay, however, on the runescape forums you will often find players buying and selling logs for a significantly larger quantity.

Also note that, whilst only members can cut maple logs, free players are currently able to burn maple logs. Maple logs may be a better alternative if you are unable to afford yew logs to burn.