After Tutorial Island

Once off of Tutorial Island, do yourself a favor and talk to the Lumbridge Guide. Read all he has to talk about, but especially the information about where to find a bank. As a new player with very few belongings, you want to protect your belongings by banking everything you don't need to be carrying around with you. Even as a high level player, I keep my inventory small and focused on the specific task at hand.

Visit the bank in Draynor Village, following the directions the Guide offered you, and stow away everything but your bronze axe. Whatever you do, don't go into battle until you've stowed away your items! Without money you can't purchase replacements, and NOBODY likes beggars. It's important to be self-sufficient and that includes being able to go on without great pain if you die and lose everything you were carrying.

Now your inventory is ready to be filled with logs that you can store in the bank until you can find a player willing to buy the logs. And for 100 logs, you should be able to get 3,000-5,000 coins! That kind of money will be great for buying armor for your upcoming battles.

You're off to a great start!