When I first hit 50, there wasn't as much content as there is now...only HM Ifrit, Garuda, Titan and The (first) Binding Coil of Bahamut, as well as some of the lv 50 dungeons (Amdapor Keep, Wanderer's Palace, Castrum Meridianum, and Praetorium). So, at the time (since there wasn't as much to do), I started my relic quest for Bard to get my Artemis bow relic weapon and did a lot of CM runs to get darklight gear so that I could have enough dps to kill Titan HM and eventually enter Coil to participate in more challenging content. They've added lots of new HM versions of dungeons since though, and echo buff/certain dungeon nerfs allows you to complete your relic quest with relative ease nowadays.

If you're interested in endgame raiding, I'd say, spend some time trying out all of the lv 50 dungeons in order get some better gear (and myth/sol tomes to buy some too), and once you are able to meet minimum requirements to enter Coil, then go for it!