Leveling first toon..gearing/questing?

[Garlyle]

Be aware that the further you go with crafting, the more difficult to obtain materials it'll expect - and so the more you'll be having to raise gathering or other crafting classes to obtain them. Don't let me completely dissuade you from crafting though, because the system for it in XIV is actually really, really fun! Just be prepared that there may come a point where the cost of materials to keep advancing your crafter's level may start becoming more expensive than just doing quests or buying them from vendors!

That said feel free to skip as many sidequests as you want. The ones you absolutely want to do are the Main Story quests (An absolutely huge amount of content is locked behind progressing or completing the main story events - pre-50, systems like Grand Company access, Retainers, and 80% of party content need story progress; and 95% of level 50 content is also locked behind completing the main story!), and the Class/Job specific quests every 5 levels (In addition to good free gear, you also gain essential skills at 15/30/35/40/45/50 from them, and you'll be expected to have them as appropriate). All others are optional.