Latin is only a very distant ancestors of modern languages, mostly French, Italian, Portuguese and Spanish.
To learn any of these languages provides the same basis to have it easier learning others.

French is relevant because the French are not much inclined to learn English but still allies and because a third of Africa understands French.
Spanish is relevant because of Latin America and because it's similar to Portuguese, which is understood in some African countries.

Russian is well understood at the NATO's Eastern frontier and Arabic at NATO's southern frontier.
Americans might want to learn Chinese because of their assistance obligations in the Northwestern Pacific, but the other NATO troops should focus on English, Russian, Arabic, French and Spanish - in that order.