Every town has a Market Ward area that is searchable for player-sold gear.

If you pull up your map, the wards are located near the town Aetherytes and have their own area name (for example: in Ul'dah they are called "The Dunes") and are marked with a little yellow arrow. When you approach the area, a menu will appear asking if you would like to go directly to a specific ward or search for an item. This Ask the Devs post shows where you can find what: http://lodestone.finalfantasyxiv.com...7cd1af570568aa You can use the search function to browse through gear available in that area. (note: Search will only show you what is available in those specific wards, it is not a global search)

Some of the side quests (started by talking to the NPC's with the "!" on the mini map and over their heads) drop rank appropriate gear, and some of the lower level (R 10-20) Leve quests will drop gear as well. This doesn't happen for every leve, mind you, so make sure to at least check the new leves every cycle to see if there are gear rewards. (Note: The gear rewards becomes more scarce when you hit the R30+ leves). Additionally, the new Mid-rank (25-35) NM's also have common and special gear drops (and accessories. SO MANY accessories, LOL). So those are some other options

My advice would be to get into a friendly linkshell. Odds are good that there will be crafters in your shell who will make gear for you if you supply the mats or sell to you at a reduced rate.