You need to go to Ul'dah since most of the population hangs out there and it's where most players sell their items. It's also where the Thaumaturge guild is so you can buy gear from NPCs there just in case no one is selling in the Market wards. To get there, take the ferry on the west side of Limsa Lominsa (an icon will pop up in your mini-menu and main menu that lets you enter the gate), or you can use the elevator in Limsa's Adventurer's Guild to head up to the top floor and take an airship to Ul'dah. You might want to set your Home Point in Ul'dah just to get easy access to most of the community.

Once you get there, head to the Market Wards (it's The Dunes on the map, it's right next to the Aetheryte) and do a search in Lower Tailor's Ward for Level 1-20 items, or Middle Tailor's Ward for Level 21-40 items. You can search in Spellcraft Ward to see if anyone is selling Thaumaturge weapons. If you have no luck here, the Thaumaturge Guild is marked on the map, in the Southwest part of the city. They sell gear your class can use at low levels, but it's usually more expensive than buying it from a player.

If you want to find a party, you can set your "seeking party" status by hitting Search in the main menu and clicking on the spot with your name. You can set your preferred class, your seeking status, and add a little message. Other than that, looking for shouts or shouting at your level range might be able to get you some people.

Good luck!