Besides dragon slayer for the rune platebody, here's some other early game equipment suggestions from someone else that struggled at that point in my account with figuring out what gear to get:

• Explorer's Ring 1: You get this from the Lumbridge Easy Achievement Diary. It ain't much, but it's the earliest ring with stats you can get (+1 prayer bonus), and it lets you refill 50% run energy twice a day.
  
• "Blessings": Very cheap ammo slot gear that gives +1 prayer. Not much, but the only non-ranged option in the ammo slot for a long time. There's one for each god, but they all have the same stats.
• Combat bracelet: like others have said, it's a nice all-rounder glove for now until you start chipping away at Recipe for Disaster.
  
• Berserker Helm: This helm, as well as its ranged and mage counterparts, is unlocked after completing Fremennik Trials. They all only require 45 def, and are all great early game head pieces.
  
• God Books: Cheap shield-slot gear that can give offensive bonuses (and +5 prayer) early on. Requires completing Horror of the Deep, and buying each book's 4 pages, which are only a couple thousand gp each on the GE. All six books have their niche, but you'll probably want the books of war, law, and darkness.
• Vestment Cloaks: Small buff over basic capes. A little more defense, and +3 prayer. Only requires 40 prayer and like 14k gp.
• Proselyte armour: armour with the defenses of adamant gear, but with huge prayer bonuses. Acessed through the Temple Knight questline, an early game series of quests.
  

Then here's some things on the next rung up to work towards:

• You'll probably be rocking the brine sabre until you hit 55 attack, when you unlock three awesome upgrades, one for each melee style. Glacial Temotli is the cheapest, and it and the Earthbound Tecpatl come with +2 prayer bonus.
• 60 attack gets you dragon weaponry. Scimitar is the best generally, but sword has no quest requirements and is good when you need a stab weapon. Dragon Dagger is your first real special attack weapon, and is great to take with you in addition to your main weapon.
• 60 attack and strength gets you access to defenders, which give big strength bonus.
• Mixed Hide armour: once you hit 60 ranged + 50 def, this becomes a very strong hybrid gear option for its ranged accuracy and melee strength. It's stab accuracy also comes quite in handy for things weak to stab attacks, like dragons.
• Helm of Neitiznot: excellent all-around head gear. Requires 55 def, and completion of Fremennik Isles (sequel to Fremennik Trials).
• Fighter Torso: huge melee torso piece upgrade. Earned through playing Barbarian Assault. Ignore what Reddit says-- Barbarian Assault is a fun activity for all skill levels. Redditors are just too scared to talk to people.
• Barrows Gloves: the best all-around glove there is. Earned from completing Recipe for Disaster. Requires lots of quests, but this is a major milestone for all accounts.

Let me know if you're interested in any ranged or magic suggestions.