The Legend of Zelda/Overworld/Quest 2

Be careful that some of the hidden rooms will charge you for some R in order to fix their doors. Avoid them.

Quest 2 overworld

 * 1) Get the Wooden Sword
 * 2) Get to the eastern Fairy Fountain
 * 3) Get some Bombs
 * 4) * Use bombs to get 30 R (on the seashore)
 * 5) * Push an Armos to get 30 R (in Green Forest)
 * 6) * Push an Armos to get 10 R (in Green Forest)
 * 7) Buy a Blue Candle (for 60 R)
 * 8) * Use the candle to get 10 R (in Green Forest)
 * 9) * Use the candle to get 10 R (in Green Forest)
 * 10) * Use the candle to get 30 R (in Green Forest)
 * 11) * Use the candle to get 30 R (on Lake Hylia)
 * 12) * Use the candle to get 30 R (on Lake Hylia)
 * 13) Buy a Magic Shield for 90 R (use the candle on Lake Hylia)
 * 14) * Use the candle to get 10 R (on Lake Hylia)
 * 15) Get to the western Fairy Fountain
 * 16) * Use the candle to get 100 R (in Brown Forest)
 * 17) * Use the candle to get 10 R (in Brown Forest)
 * 18) * Push a tombstone to get a Heart Container (in the Graveyard)
 * 19) * Enter a crypt to get 30 R (in the Graveyard)
 * 20) Buy a Blue Ring (on the seashore)
 * 21) Get the Power Bracelet (on Death Mountain)
 * 22) Get the letter (use Power Bracelet on Death Mountain)
 * 23) * Use bombs to get 30 R (on Death Mountain)
 * 24) Buy a Red Potion for 68 R (use Bombs on Death Mountain)

Summary
This is all that can be collected before Dungeon 1, and it's clearly less equipment than in Quest 1:
 * 4 Heart Containers instead of 3
 * Wooden sword
 * Magical Shield instead of small shield
 * Blue Ring
 * Bombs and Blue Candle
 * Power Bracelet and Red Potion (difficult)