Naming substituted bicyclo compounds
You have already correctly identified the parent structure of the compound as bicyclo[2.2.2]octane.
The most important simplified criteria for the numbering for such structures 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;
(…)

The compound that is given in the question doesn’t have any principal characteristic group that is expressed as a suffix. Thus, Rule (c) is not relevant in this case.
The compound also doesn’t have any multiple bonds. Thus, also Rule (e) is not relevant in this case.
Next, low locants are assigned to the substituents that are expressed as prefixes according to Rule (f). Note that all substituents are considered together in a series of increasing numerical order. Therefore, the correct name is 5-bromo-2-chloro-7-fluorobicyclo[2.2.2]octane rather than ‘2-bromo-5-chloro-8-fluorobicyclo[2.2.2]octane’ since the locant set ‘2,5,7’ is lower than ‘2,5,8’.

Only if there is still a choice, a low locant would be given first to the bromo substituent in accordance with Rule (g).