That depends on what you mean by "benefit". If you mean "some gear that will statistically improve my character for end-game play", then no. For gear, item level usually trumps all other considerations - so the gear you get at end game will be significantly better then anything you can get now(though keep upgrading your gear - trying to go all the way to 70/80 with only level 60 gear is insane). If instead of gear benefit means "learning to deal with mechanics i will see in the future", then maybe you should consider branching out some. Attacks that originated from optional trials and raids find their way into mandatory content more then you might think. However, if you learn quick you can probly get away with skipping the optional stuff until later and just pick up the important dodges/techniques via MSQ content. If benefit means "see interesting parts of the story, expand my glamour options, and get some new mounts/etc" then OMG you need to get into some optional content ASAP. That could mean leveling a racing chocobo/getting a good triple triad deck so you can save up for the Fenrir mount, it could mean working on beast tribe faction so you can make a turtle glamour, it could mean playing older raids so you know what really happened during the calamity and more history of the world. While the possibilities arent endless, there sure are a lot of them for this category of benefit.
Although, one thing you should for sure be doing. At a minimum try to get both challenge log entries done for your chocobo each week(this of course is assuming that you unlocked the challenge log, and did the quest to teach your bird to fight - if not then go do both immediately... log is in limsa, the bird quest is in south shroud). Birds take an eternity to get through some of the higher levels, and having a bird that can at least competently heal you when out solo can make a world of difference(or for our healer friends, a bird who can deal damage for you). And youre already doing it, but keep up on your job quests too. Some important higher level abilities are only unlocked once youve done the proper quest.