Welcome to Eorzea!
With the addition of the World Visit system that allows you to freely travel between different servers on the same data centre (with limitiations), it's meant servers have started balancing out, but as a general rule the server I'm on (Balmung) is usually regarded as the most busiest and heaviest populated server in the game (even more than the JP servers) - this is because it was originally considered the unofficial RP server back in the original version of FFXIV (version 1.0) so everyone flocked there when FFXIV ARR launched, even those who weren't into RP (I moved to it to join my friends who were long established here, having started on the JP server Ridill). But because of that Balmung has long been locked to new players and even transfers, save for some exceptions, so it's very difficult to get onto now sadly.
Because of this RP communities have started appearing on other servers as well - Mateus I hear is now the second RP server with a very large and active RP community so that might be an alternative. I haven't heard much about Brynhildr other than it's a relatively small and quiet server, but that's not a bad thing! Location doesn't really matter too much as all NA servers are in the same physical location (originally it was Montreal in Canada, but as I understand it SE moved them to somewhere else.). I live in Australia and have not too many issues connecting to a NA server.
Either way, if you're unsure whether your current server is right for you, try visiting another server by accessing the aetheryte in your starting city (Gridania in your case) and select 'Visit Another World Server' and choose a server - be aware that there are some things you cannot do or access while visiting another server. This page details the system further. Incidentally Balmung and Brynhildr are on the same data centre so you can visit Balmung if you wish.
Once again, welcome to FFXIV!![]()