WoW: Classic is scheduled for August 27 (technically August 26 if you're in the Americas). The soonest that you can play it is starting in May, during Blizzard's scheduled stress tests. To opt-in you must have an active subscription on your Battle.net account. If you do, go to Account Management and select the Wow Classic beta. Keep in mind, there will be level caps during the test. The schedule is as follows:
Unlocking the Lightforged will require you to complete the aforementioned Argus storylines and earn the “You Are Now Prepared” achievement. In addition, you’ll have to earn Exalted status with the Army of Light. As with the Argussian Reach, this one could take a couple of weeks, as it is time-gated. However, the main story quests should help you at least reach Friendly status with the Army of Light.
Only really to expand on Gráinne's comment as regards the 'collecting' and 'roster development' sections - which are, as said 'distinct' although they are intrinsically linked - I would like to point you in the direction of the in-game Achievements > Battle Pets > Collect tab. There are a series of achievements called Raiding With Leashes, pretty much all of which can be completed via the auction house - if you have the gold/inclination - or by completing old raids.