As you can see, most Achievement Diary rewards are focused on RuneScape gold increasing gains from various abilities - that's why numerous players take it as soon as is possible. When you start doing Achievement Diaries early in the game, you will gain some time in the end since different shortcuts, teleports and exp increases will quickly fill in the time it takes to finish diaries.
If you are ready to work on them in those initial stages of game, you may come upon some difficulties that are greater difficulty. If this is the case with you, make sure to go through the easy stages and come back to the tougher ones when your skills are high enough. Quests can be especially helpful for this since they might grant you experiences in the specific skills you need to raise.
Depending on what you need and the goals you wish to achieve, different rewards could be ideal for your character's development. However, there is one especially popular with adventurers in OSRS that is Explorer's Ring from Lumbridge Draynor Diaries. It provides extra run recharges of energy. Gielinor is a huge continent and has many places to visit.
Energy for running can be the primary supply in your arsenal. Moving faster to the desired places which means more quests are completed faster more experience-based, quicker farming, shorter Treasure Trails, and more enjoyable time in the game overall. To top it all off, Lumbridge and Draynor diaries are renowned for their minimal requirements to runescape 2007 gold complete, but they do require the Recipe for Disaster as well as at least 88 levels in the Smithing skill.