1) Go to the shops, and buy a Bronze axe from nurmof. *Shouldn't be too expensive.
2) Then take your axe to Catherby. There you will find a conveniently located oak tree near the bank.
3) Cut the Oak tree until level 30, then make your way to draynor.
4) Draynor contains willow trees, that are placed right next to a large bank. you can cut your logs, and bank em' in the same place.
5) Once you reach level 60 woodcutting, you can then cut yew logs. Cut yew logs until level 70.
6) At 70, you can cut MAGIC logs. Cut Magic's until you've got your 99! Skillcapes are in the shops. Trade BOB.