This game lets you freely try all the classes, alternate between them, and advance any or all you wish to, so you aren't locked into the class you begin the game with except for the first 10 levels. (It's your level 10 class quest that unlocks the ability to add other classes.) I recommend at least trying all of them. Once you've advanced each of them a bit, you can decide which ones you enjoy enough to continue them through the later levels.
As for group/solo content, there's a mix. You'll need to advance the main scenario in order to unlock content. It alternates some group dungeon runs with a lot of quests designed to be run solo but that could be done in a duo with someone if you want (or technically even a full group, though that would be overkill) and occasionally some short solo-only instances. The dungeons, however, once unlocked can be repeated as often as you like. Repeating them is done either to get better gear or gain XP, but it's also one of the primary ways you get more group play opportunities, as the dungeons require being done in a group. (4 players for early dungeons. 8 for some of the end-game dungeons, and some end-game raids with I think it's 24.)
There is also open world group content (FATEs at all levels and Hunts once you get near level-cap) that's not linked with the story but can offer some nice rewards. And it's rather fun to tackle a huge monster along with a hundred other players all going after it at the same time (provided your computer/console can handle displaying everyone at once - some lower-end machines have issues with that). It's only once you get near end-game that you're likely to see the really crowded ones like that, though. Earlier FATEs can be done in a group, and you may see a couple or several other people involved in it as well, but the sort that draw in what seems like half the players on the server are level 50 stuff.