Inventory management is the not-so-secret end boss of FF14. No amount of space is ever enough, so it's unfortunately up to us to thoughtfully manage our items so we don't end up full and then have to spend hours cleaning our figurative rooms. A couple tips:
If you don't need something, get rid of it! Armor you're no longer using, crafting items you think you might use someday, etc. Marie Kondo has the right of it: look at each item you own, and ask yourself whether it's truly worth the inventory space it's occupying.

If you decide to get rid of something, sell them via your Retainer on the Market if they'll earn you some decent cash, otherwise just sell them to a vendor or discard them.

In case it's not obvious, you can move the gear in your armory to your other inventories as well. So if you have gear you're not actively using, but you want to save it for another job you're leveling, you can store it in your retainer, etc, until you need it.

With the exception of your primary combat class, I recommend only updating your gear for a class every 10 levels. You don't need to keep around boots that are level 31, 33, and 37; the increase in stats is generally not going to make a meaningful difference. Getting rid of this "inbetween" gear will help keep you uncluttered.

Don't forget to store gear that you're only keeping around because it looks cool in your Glamour Dresser, which can be accessed at any inn. You can then make your new gear look like the gear in your Glamour Dresser, without having it in your actual armory.

If you're feeling very low on cash and resources, you can find out how easy it is to replace gear by looking at the details listed below its stats. If there's a "Sale Price" (not "Sells for"), that means that's the price to buy the item again from an NPC vendor. If it doesn't have a Sale Price, that means the gear is either crafted or drops from a dungeon or something. You can check the Market Board for items like this, which will give you the going price if it is crafted gear and if it's not listed then that means it probably comes from a dungeon, which generally means it takes a little luck to replace it.

And in the end, don't stress too hard about whether it's okay to get rid of something. Most items are either garbage or easily replaced, and the more you play, the more money and strength you'll have to easily replace them.
Best of luck!