This is a good summary.
Some extra things:
About the dragons:
Which ones spawn is semi-random. There is no strict order of priority, which ones you want the most depends on which champions you have.
Fire drakes are great for champions who build a lot of AP or AD (since it's a percentage increase), but not so good for champions who focus more on CDR / AS.
Ocean drakes are great for poke (either poking, or being poked.)
Cloud drakes are great for assassins and initiators.
Mountain drake is just great for taking/securing objectives faster. It's generally useful, but has no combat application unlike the other three.
Items have changed a lot.
Mage and ADC items, especially. Pretty much everything on the mage side has CDR on it now. Hourglass is now a cheaper item with CDR and a much longer cooldown, for example.
ADC itemisation also has a lot of CDR in it, through Essence Reaver which gives you CDR when you build crit, though mostly people just rush Hurricane now to apply the Fervour mastery faster.
Warding is very different. You can't buy normal wards any more at all. You can only place them through a warding trinket, which has limited charges and a much shorter duration early-game. Only Sightstone and one of the jungler items lets you place wards otherwise.
You can buy pink wards, which are now 75g, but are permanently visible. They have 5hp and regenerate lost health. Each player can only place one pink ward at a time, and carry a max of 2.
happened.