(Not saying I am correct) I would start off with the butyne chain and place the triple bond first then number everything else relative to that
1-butyne (see
http://en.wikipedia.org/wiki/1-Butyne) or but-1-yne
1-butyn-4-ol or but-1-yn-4-ol
3-chloro,1-butyn-4-ol << my attempt or 3-chloro,but-1-yn-4-ol
E-Z not relevant in this case I believe.
The following is probably as comprehensive a guide to organic naming as one could tolerate
http://www.acdlabs.com/iupac/nomenclature/I think that there is some flexibility in organic naming as long as the resulting name is unambiguous , i.e. defines the structure precisely.
Clive