Specific search for subcategiries

I want to create such a categorization for search:

kennel -> dog -> dog breeds (1, 2, 3….) via autofill (400 titles) -> city = serch
kennel -> cat -> cat breeds (1, 2, 3….) via autofill (100 titles) -> city = serch

and position this search like on this site http://www.childcarefinder.ie/

Example: select ‘kennel’ then ‘dog’ then write ‘dog breed’ for example “spaniel” then ‘country’ or ‘city’ and click ‘search’. Than I see listing with dogkennels in this city or a country with breed spaniel.

How I can do this with filters or another functions?

Thanks!