Prioritize skills required for quests, most quests have great rewards. If you plan on training combat, do it through Slayer since it is a 120 skill.
Melee
Bandos Helmet, Chestplate, Tassets, Gloves, and Boots
A Godsword, preferably Saradomin. Dual wield weapons, Abyssal Whip and Dragon weapon will do for now.
Fire Cape or Obsidian Cape
Magic
Subjugation Hood, Garb, Gown, Gloves, and Boots
Polypore Staff or Staff of Light
God Cape
Ranged
Armadyl Helmet, Chestplate, Chainskirt, Gloves, and Boots
Armadyl Xbows and your pick of either Runite Bolts or Broad bolts
Ava's Acumdumpster
Learn EoC. There's a tutor north of Lumbridge who will teach you the basics of EoC. Outdated but it still works. Set your action bar to Revolution, this mode will automatically use your basic abilities if they aren't on cooldown. It may take awhile to get the hang of it, but if you're confident enough, you could go Full Manual.