Milestones do reset every week. This includes your Flashpoint (doing public events on a designated planet), Call to Arms (play PvP if you want to or not), the Nightfall (which I'll be looking for some after work around 5:30 EST), the raid, trials, and (which you'll get by doing just some of the previous) - personal clan XP. All of those will get you luminous engrams (listed as "powerful" gear for rewards). The only ones that don't reset are things like the exotic weapon quests.
Do pick them up by the end of the week - certainly (although I've heard tell that they get sent to your postmaster if you don't)
However, just be thoughtful on when you turn those in....
If blues and legendary engrams aren't going to give you an upgrade - turn one in
Do blues or legendary engrams do anything for you now? If yes, use those (including tokens on planets, with Vanguards, etc) - If not, feel free to pop another luminous
Lather, rinse, repeat
While I haven't actually finished one myself (yet), I also understand that there are drops for both the normal and prestige Nightfalls - hopefully I'll find some a team and knock at least one out this week.
The clan engrams - I think they're just slightly better than normal legendary ones - but if some of those are available - might be worth turning those in before hitting the luminous ones.
Bottom line is once blues and legendary gear stop progressing your character, you'll need either a luminous engram, and exotic engram, or raid gear to further that progression
And unless you're just jumping in for less than an hour - do yourself a favor and always run with a Fireteam token thing active - they're 50 bright dust which you should have plenty by just breaking down additional ships, sparrows, and ghosts that you're earning from bright engrams (which will not progress your character's power levels)