With all of the bots and so many players in the beginning areas, do you absolutely have to do the quests (will i be missing anything good? special potions, gear, adena?) or can I just find a nice spot and start grinding like in classic?
only quests you "have" to do are the transfer quests,
(well actually, you don't have to do that either, but w/o the skills from more advanced jobs kill something become more difficult :D)
No you dont, when you hit 18 you go where Lord kakai is(Talking island) and speak to class master of your class to start your 1st transfer change.Same thing wit lv38 for second change but the masters are in gludio this time
can I just find a nice spot and start grinding like in classic?
Of course you can, just remember that by doing the beginner's quest chain you get to lvl 40 in under 2 hours while grinding like in classic may take a few times longer.