What is the IUPAC name of the given compound?
As for your other question, the simplified criteria for the numbering are:

lower locants for the principal characteristic group that is expressed as suffix
lower locants for multiple bonds
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name

The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:

P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(…)
(c) principal characteristic groups and free valences (suffixes);
(…)
(e) saturation/unsaturation:
  (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)

For the compound that is given in the question, you have correctly identified the principal characteristic group as ketone. It is expressed as suffix “one”. Thus, a low locant is assigned first to the ketone according to Rule (c), which yields “…1-one”.
Next, a low locant is given to the double bond according to Rule (e), which gives “3-en-1-one”.
Finally, a low locant is assigned to the remaining $\ce{-OH}$ substituent according to Rule (f).
Thus, the complete name is 5-hydroxycyclohex-3-en-1-one.
Rule P-14.4 applies to chains as well as rings.