Just as wool from different breeds of sheep spins differently, different cotton varieties
spin differently.  Here are a few different varieties I have spun.  Freshly carded punis
seem to spin a little better than sliver or the punis from India.
Upland cotton is one of the more common
varieties you will find in the United States.
 It is all around a good spinning cotton.  
The natural brown variety I got as raw
cotton, so it shows a hand carded puni.  
Pima cotton looks and spins
much like a cotton/silk blend.  
This long stapled cotton is soft
and slick.  I will repeat advice I
have read elsewhere on this
breed, this is not a beginner's
cotton.  Gain some experience
with cotton before you tackle
this one.
Acala is the easiest to spin cotton I
have tried.  It seems to have a bit of
crimp to it, and drafts easily.  This
cotton is the one I would recommend
for beginners.
Sea Island cotton is one of the rarer
varieties of cotton.  It is easier to spin
than pima and makes a pretty, fine
yarn.  I carded this after carding some
red cotton, so minuscule bits of red
got mixed in, then tied it with some
hand dyed blue cotton yarn for
boiling, so some dye transfer
occurred, which made an interesting,
speckled yarn.
I am not sure if this one is an actual
variety of cotton, or just where it
came from, so I included it here.  
This cotton is easy to spin, creating a
nice yarn.  
Cotton Varieties