paragraph when using \head, but there is when using \item. How can I make
that by \item the first paragraph also has no indentation?

See
http://wiki.contextgarden.net/Indentation#Setting_up_indentation_inside_environments

What you need is

\setupindenting[big,yes]
\setupitemize[1][indenting=next]

\starttext
\startitemize
 \item \input knuth
\stopitemize
\stoptext

Does not work. I tried:
  \setupindenting[yes,medium]
  \setupitemize[1][indentnext=no]
  \setupitemgroup[itemize][indentnext=no]

  \starttext
  ` Backtick\crlf
  ' Apostrophe\crlf
  ‘ Open curly quote\crlf
  ’ Close curly quote

  ‘some quoted text’

  “some doublequoted text”

  \setupbodyfont[palatino,rm,12pt]

  ‘some quoted text’

  “some doublequoted text”

  \startitemize
  \item Alleen een test

  \input knuth
  \stopitemize

  \stoptext

But the first paragraph is still indented.

I still find it strange that \head does not indent the first and \item does.
I would expect them to behave the same.

 When using \startitemize … \stopitemize there is no indent for the first

Well, you did not add indenting=next key....