The word you're looking for is pneumatology, the study of the Holy Spirit. Pneumatology and (the somewhat archaic) pneumology share the same Greek root 'pneum', meaning breath or wind; the first usage is metaphorical (Spirit as the breath of life) while the second is literal (the medical study of the pulmonary organs). Confusing, yes...
There are some things all graduate programs in philosophy in the US/UK are looking for:
Strong analytic skills
Basic familiarity with logic
Good writing in English
Good grades in classes (especially classes that show reasoning skills)
Strong writing sample (demonstrates 1 and 2)
Where things will differ,
For history oriented programs, you're definitely ...