21st C Type Set

The way I see it:

Cents (3, for now): Lincoln Memorial, One Lincoln Bicentennial, Lincoln Shield. One could expand this to include all the 2009s, if desired, and the coins are easily obtainable. This would bring the count up to six.
Nickels (4, for now): Jefferson Monticello, Westward Journey 2004, Westward Journey 2005 (because of the different obverse than before), Return to Monticello. Again, the other Westward Journey nickels from 2004 and 2005 are easily obtainable, so the count could expand the number nickel types to six.
Dime (1, for now): Roosevelt
Quarter (4, maybe 5): State Quarter, Territory Quarter, National Park Quarter, 2022- Crossing the Delaware Quarter. I wouldn't be surprised if there are special designs for the Washington Tricentennial in 2032.
Half (2, for now): Low Relief (Used through 2014 circulation strikes), High Relief (2015-Present for circulation strikes, though a disinterred 2014 Anniversary Set coin would fit the bill here)
Dollar (3, for now): Sacagawea (2000-2008), Presidential, Native American (2009-Present). The Native American series will probably continue past 2016, if it doesn't revert to the original Sacagwea reverse and plain edges.

do we really need every quarter?

Well considering the entire reverse it different on each one I would say each one is a different type. Same series but different type. Would you consider a draped bust small eagle dollar and a draped bust heraldic eagle dollar to be the same type? After all they both have the same obv. (If so that would make the early ype set a whole lot easier and cheaper. Especiallsince you could say the same thing for the half dollars and avoid that 1796 and 97 small eagle half dollar)

No I would say if you want a COMPLETE 21st century type set you need ALL the quarters and President dollars.