Since it sounds like you're brand-new to being level 80 you probably won't have many Allegory tomestones yet, but focus on getting those and spending them on the i490 tomestone Crystarium gear set in Eulmore. (Yes, it's a bit weird they sell Crystarium armor in Eulmore. I got it over it.) This will be the highest gear available to you without doing any raids. There is a weekly limit on it, so focus on getting the cheaper items first to squeeze more items out of it per week. It's usually possible to get 2 or 3 items each week for the first three weeks or so. You won't be able to get the weapon from this set without raiding, so don't bother with it.
If you've reached the point that you can do the new 5.2 relic quest, it is super easy, quick and best of all dirt-cheap. For 1000 Poetics tomestones you can get an i485 Resistance weapon with 5 materia slots. If you do nothing else, do this and do it first assuming you've progressed in the story far enough to unlock it. It's the best gear slot, the highest ilevel weapon you can currently obtain without raiding, and it's essentially a free relatively high ilevel item. If you don't have this unlocked yet, then just get the highest level crafted weapon you can afford. All of the other weapons require tokens of some kind from raiding. Last resort if you can't afford a crafted weapon is to get the i430 AF weapon from Grenholt sound of Ondo Cups in The Tempest for a small amout of gil.
Before the Crystarium gear you can buy crafted i480 Neo-Ishgardian gear from the marketboard, craft them yourself, or have players craft them for you.
If you can't afford that or don't know anyone will help you out with free crafted gear, then you can spend Phantasmagoria tomestones in Eulmore to get i460 Deepshadow gear. You can upgrade these to i470 Augmented Deepshadow gear fairly easily, albeit with a weekly limit on drops, by running The Copied Factory.
Don't bother with any lower level gear unless you've run out of tomestones and/or gil completely. In this case, your last resorts are i460 YoRHa Type-51 gear drops from The Copied Factory, i455 Warg dungeon gear from Anamnesis Anyder, crafted i450 Facet gear, i445 Warg dungeon gear from The Grand Cosmos or again the absolute last, last resort i430 AF gear set obtained for a tiny amount of gil from Grenholt in The Tempest.
You can see a full overview of the level 80 gear below for reference. Just ignore everything in the weapon section if you can get a resistance weapon right away.
https://ffxiv.consolegameswiki.com/w..._80_Gear_Guide