Question: Is it best to double down on a sponsor's bonus when picking cargo, virtues, tech, ... or diversify?
Probably the best (but least useful) answer is "yes" (since your question has an "or" in it). Just as in other iterations of Civ, you always have the question, should I double-down on my civ's unique attributes/units or should I use those unique attributes/units to buy some time to pursue a different path?
The classic CiV example is: should you open Honor when playing as Aztecs? On the one hand, you want to farm barbs as Aztecs to generate culture, so perhaps you should open Honor for more culture from barb kills, the barb combat bonus, and better knowledge about barb camps. On the other hand, perhaps you should ignore Honor and use the Aztec's culture-from-kills to motor your way through Tradition all the faster, to start farming the Aztec's real bonus -- potentially superior population growth, yielding better science, etc. Having thought about that one at some length, I think the answer is "Yes" to both, depending on what you want to accomplish, what the map looks like, and your difficulty level (e.g., on Deity, the AI will clear most barbs before you know it, so culture-from-barb-kills is going to be much less significant than it is, e.g., on Prince).
Of course, in BE, you won't know the map before picking cargo, etc., so the decision is probably more difficult than that example would imply.