The extreme trials and savage raids require coordinating your team with voice chat (discord), as well as spending time outside of the game studying the mechanics of the fight if they aren't new releases. If that sounds daunting to you then don't sweat it, they're completely optional and unnecessary. You can do all of the other content just fine with the latest crafting gear that you have. Also, the extreme and savage fights do not offer any additional lore/story content, and so you won't be missing out on any lore if that interests you.

If you want to improve in other ways such as acquiring fancy mounts, minions, titles, gil, and other rare items then I recommend looking into Palace of the Dead, Heaven on High, and the Bozja Southern Front. Bozja in particular is one of my favorite side-contents to do because it allows you to change the playstyle of your job (e.g. with certain items tanks and healers can become dps). If you like to play solo then you may enjoy trying to complete floors 1-100 in Palace of the Dead by yourself to get the "Lonely Explorer" title (but you can also complete these floors with a party to try and get the rare items in floors 100+).