Full Servers
If you are only doing PvE you don’t need to be on the same server, just in the same server grouping (EU or NA). This is because of Megaservers.
https://www.guildwars2.com/en/news/introducing-the-megaserver-system/
And how partying up works.
http://wiki.guildwars2.com/wiki/Party
If you are in the same party and go to a map it will try to put you on the same shard. If it doesn’t and If you wish to go to the world that another party member is in, right click on their portrait and choose Join In, and you will be moved to their world.
The only time servers are really important is for WvW reasons.
Tarnished Coast rarely drops below full. But, as explained above, you need not be on the same server to play with your friends, except for WvW.
You can transfer to any server that is not Full later, either at a cost in Gems, or at no cost by deleting all your characters and just moving your account. You can do this once every 7 days.
Welcome to Tyria, and happy adventuring! =)