Good advice above. It really depends on your goals.
If interested in different preamp sonic colorations and/or subtle detail and imaging differences (which are certainly audible, but relatively minor compared to the microphones, microphone setup, and position in the venue), I suggest borrowing a few different preamps to get a feel for how their inclusion in the signal chain differs from going direct into the recorder. The exception is the DR2d which will require an external preamp in more cases. The internal preamps of the DR-680mkii are on the "clean and mostly character-free" end of the flavor range, and most of the preamps you list are somewhat similar in flavor. Of those listed, I imagine you'll probably hear the biggest tone-color difference using a transformer based preamp such as the Areco.
I'm satisfied going direct into the DR-680mkii, so these days I mostly reserve the V3 for when I need to leverage it's digital output to record an additional 2 channels if I already have 6 going in analog directly.
Strictly sound-wise, I do prefer using the V3, but not enough so to justify it very often except as a way to get those extra channels recorded. That's mostly for practical reasons- it requires significant bag space itself, requires separate powering (and bag space for that), generates sometimes problematic waste heat, and requires additional interconnects which represent potential points of failure. I have enough to deal with recording 6 channels, and the simplification of eliminating all that extra stuff trumps the sonic advantages in most situations for me. So I mostly choose to it when I need it's phantom power or digital output (practical reasons).
I have no problem manipulating the sound afterwards, so I also prefer "clean and clear" to "warm and goeey" in the raw recording because it limits my options less. I can make it warm and gooey after the fact, but can't easily do the reverse, if at all. But if you are searching for a particular flavor in the raw recordings without further manipulation, an appropriate preamp can provide the most appropriate icing on that mics/setup/location layer cake.