+ I am looking at a new LC III and a used IIci.  Prices

+ The IIci has much greater potential for expansion, a la NuBus and
+ greater memory capacity.

How important is this? How many NuBus cards do you have/plan to
acquire? How much memory do you really need? I've got a ci, and
20mb of ram. That's plenty. I also have a 24bit graphics card
on the NuBus - I'm a sucker for pretty pictures...I think the
LCIII can have a bootable ramdisk in memory, which a ci can
not have. At least, not out of the box.

+ The LC III would be new, under warranty, newer ROMs (is the IIci
+ "32-bit clean"?), and would have sound input.  I also like the
+ "pizza-box" case.

The ci is 32-bit clean. I solved the sound input problem with
a MacRecorder. But that's gotten to be a fairly expensive
solution now that Macromind owns MacRecorder.

+ Performance-wise, I have read that they are almost identical, the
+ LC III being a little slower.

The actual difference is probably not worth worrying over.
 
+ So, which should I get?

Depends on the price you can get the ci for. Educationally speaking,
the 4/80 [?] LCIII here at FSU can be had at just under $1300. Add
in roughly $500 for a monitor. Last I'd heard, an 8mb LCIII simm
went for ~$250. 

I think you're in a win-win situation. No matter what you decide,
you'll most likely be happy with it.