First of all, there is also supercontainers and gift containers just for playing higher tiered ships. But if you want more challenge and a guaranteed rewared - there are Directives.
And the Directives aren't too hard. Of course, for a really new player they can be challenging, but for anyone with more than a single ship line with tiers higher than 6 they should be reasonable.
Almost all tasks can be done in Co-OP, and all tasks are done with T5+ ships. Let's look at 4th stage, which should be the strongest, constists of:
1) 1500 hits with main guns or secondaries - basically can be done on anything in coop, battleships and destroyers allow it to be done in several battles.
2) 600 000 damage to ships. - It's also quite doable.
3) 60 000 exp - 40-80 battles, less with premium time. Will be done anyway while you're completing other missions.
4) 9 000 000 potential damage - this may require fast destoryers, but BB's are okay.
5) Spot 65 torps - also best to do in DD's, but being a target - BB/Cruiser with hydro can also help.
6) 20k free exp - you'll need some flags to do it fast, but nothing too hard.
7) 100 Citadel/Torpedo hit/Flooding/Fire ribbons - okay - this may take some time, but the ribbons are being collected with any ship.
8) Destroy 25 ships - again - 25 battles at average should be okay.
9) earn 2 500 000 credits on Japanese ships - this may require some grind, but for some people it may be extremely easy.
10) earn 2 500 000 credits on Pan-Asian ships - similarly, though there is less chance you'll have Pan-Asian ships, since right now there is only a single DD line.
11) earn 2 500 000 credits on Pan-American ships - okay - this mission is to thank guys with Nueve.
You need only to complete 7 from those missions and anyone can do 9 of them with some effort. 10, if you have Pan-Asians researched (I highly recommend at leat getting to Gajah Mada - deepwater torps give unique gameplay and they aren't bad with guns either).
And most of the missions will be completed in parallel.
Does it all require some effort? Yes. Can it be done in a week - sure.