Getting started...

[Raldo]

You can solo all the way to 50 (mainly using leves), although it is faster to level up by slaughtering groups of monsters in a group (people start grouping around 20~30). You can also be powerleveled, if you're into that.

Unfortunately for partying, there are a few things working against you.
1) There currently isn't a large influx of new players.
2) A lot of people have leveled what they want to level.
3) Since you can solo, some people choose not to group at all.
4) The search system kinda sucks and isn't used much.

I haven't leveled anything in a while, so I can't really comment on the current status of the leveling scene (plus I'm not on your server), however people used to just shout in Ul'dah for parties.

If you continue solo (or even in a group), there is a dungeon called Sposhae, East of Limsa Lominsa, that is an "open-world dungeon" that might spice up leveling if leves are getting boring.