Is there a self-consistent citation system? I study undergraduate philosophy. My school of philosophy allows its students to use whichever citation style they prefer to use. I've used a few different styles; however, I haven't yet found a methodical one. 

I'd prefer to use a style enables the user to derive the formatting for any given type of reference (e.g. a website, or a paragraph from a printed publication of a compilation of translated public-domain articles) from a set of just a few rules.

Do you know of a system like that?
Work out which journals you are most likely to be publishing in. Read their authors' guides. Pick the citation style that occurs most frequently.

Start using that now.

That way, you'll have all the tools you need in place for when you start submitting to those journals.

I think reference management software these days typically includes the ability to incorporate new citation styles, often encoded in CSL (Ctitation Style Language), as well as having the most commonly-used ones built in.

Any decent reputable citation style will be internally consistent enough, and will have rules for papers, books and various species of grey literature.