If you prefer pve, Look in in recruitment chat to run gen and laz dungeons to get your expertise up to 600. Each run you will 6-8 expertise bumps. Can be 600 in all weapons and armor in a few weeks. Then you can focus on running mutations for shards to upgrade from 600 to 625. Make sure you grab the expedition faction quests before running the dungeons to get faction tokens…
If you are pvp, work on the pvp track by running faction missions in GC, oprs, or arenas.
If you are pvx, definitely start with dungeons as they are the quickest way.
Yeah gs requirements for regular dungeons are pretty low. Most groups running regular dungeons don’t even ask for gear score… they are only running to get their gs up too. Many of the group will be over geared for the dungeon so the dungeons will be pretty easy for the group.
You can buy GS590+ gear for cheap at AH, so your GS gets bumped around 540-550, this is sufficent for Lazarus and Garden.
For Tempest you’d want a little bit more GS, like around 570.
Take a look at the Gypsum system, its another way to Bump your expertise. Use it for your weapons and jewelry.
Truly solo, I think only ninja chest runs in elite areas, unfortunately. There are also some bosses you can solo, but it takes too long most of the time. Both alternatives are not very efficient and boring after a while. But random 5 man group at Laz/Gen is easy nowadays and barely needs any interaction because most players are experienced at them.