Welcome to Eorzea!
1. Aetherial gear (pink) is fairly easy to come by and will spirit bond quickly as well, I'd recommend making materia to either meld to other gear (if you're into that) or to sell. In general gear will sell better in materia form than to an NPC (once you've worn the gear and fought you can't sell it to other players). If you haven't worn the gear yet it might sell better as is. Should you sell it would depend on how hard it was to get and how soon you will be using it again for another class. I for example leveled all my jobs to 50 almost as one unit and recycled a lot of gear, replacing my recycled gear with pink spiritbond gear to sell and then going back to my recycled equipment. After you've used the gear for stats you have one last concern before converting or selling them, would you like to use it for glamour later (for its looks)? A lot of people will keep certain pieces of equipment so they can use it for glamour later (you must have the item to use the item's image).
2. Use the gear that has the better stats, Aetherial gear will in general be better than white or green gear of similar levels - green gear generally looks prettier and white gear is just stuff, unless melded a whole bunch it will likely be bad stuff (or HQ'd). If you get two pieces of the same gear after you hit 100% you can switch to the other and do the same*, this can make you some gil. * (good idea for pink gear, which can't be traded anyways, may be a bad idea for white/tradeable green gear)
3. It offers decent exp and efficient exp perk if you're already in the zone for quests, and will get you a ring once you complete it all the way. It isn't required though.
4. I would continue the main story line once you hit level 50, the level 51 quest will not reward gear better than the level 50 raid content - however it is not required to have the better gear to move through the story. Gaining that edge may take longer than just going through with handicap story gear :P (also the gear granted isn't that bad, lol).
You can always come back to the old raid content unlevelsynced with one or two people and face roll it for the items and story :P.