No random battle option: rent a car for 3,500 gil and walk on train tracks, then, walk on paved roads or get Diablos' No Encounter ability. That’s it!
Free Potions in Timber Town: ypu chould get Rinoa in the party. After that, go to the bridge and return. Repeat this as many times as needed to make a man appear. Then, you have to talk to him 2 times and you will get a Potion. Leave the screen and return until he appears again. Repeat the trick to get more stuff.
Easy Ability Points: you have to go to Cactaur Island and get 20 AP for each Cactaur you kill while in battle.
Easy Experience Points: display the world map and go to the left-most island where you can find monsters. These monsters will help you to get experience points after battles.