Level all 5 factions (including cryptarch) to the point just before levelling up. If you do this right you will have 15 different packages to open on HoW day, after finishing the level off with bounties etc.
5 on each character including cryptarch levels. Assuming you have three characters. It will take some work but you should be able to do it in the three weeks or so before HoW drops.
In summary, level New Monarchy, Dead Orbit, Future War Cult, Vanguard and Cryptarch to just before levelling on each character.
Obviously there is still a chance you'll get nothing decent but at least it might give you a small head start.
Edit 1: I forgot Crucible as a few have mentioned, thanks for the reminder.
Also, some have mentioned saving engrams as that will help level Cryptarch, though you won't get any new gear from the engrams.
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Also, stockpiling commendations is a great way to get rep too. Idk how many people know this but commendations are getting cut in the HoW release and all existing ones become consumables that give you 250 rep each.