Your first priority as a new play should be levelling your character class and completing the Main story quest (quest icons with sun blaze shape).
The vast majority of the player base is at the current end of the main story.
The story and side quests are generally a solo activity, while people parties for dungeons/raids/fates/hunts/etc....

Do every quest you come across, as this will unlock several things. Check the Recommendations every time you enter an area for available quests.

Use the duty finder for random groupings.
Use the party finder for specific activities - usually end game raiding of nature or another.

You have joined a very large FC, which is usually a good choice for a new player.
Ask your FC for a crafters to make you levelling gear. An FC crafter will usually charge you 1/4 or less sometimes the Market Board price for HQ gear; not that you really need HQ gear, it just makes things easier.
Ask your FC to take you through each dungeon the first time you unlock it. These days, there is very little shortage of "helpful" high level players because of the bonus available from your first completion and the rewards they get related to the current Relic weapon quest.