That’s a really good question, almost every speller wrestles with it sooner or later. Although there’s no set formula for an order of study, a good place to start is by looking at the odds of getting a particular language at the national spelling bee. According to Scott Remer in his book “Words of Wisdom,” (which I recommend highly), here are the languages of origin ranked according to percentage of words in the Scripps National Spelling Bee:
Note that the first four make up the majority of words; I would suggest starting there, and then allocating appropriate study hours to the remaining languages.
Another thing to consider is studying roots: take a look at Merriam-Webster’s Dictionary of Prefixes, Suffixes, and Combining Forms: I would rate that as important as any of the languages listed above.