Future Oxford/Said Business School Applicant

I am interested in obtaining an MBA further down the road. My reasoning for waiting pertains to my lack of relevant work experience in the business field. I felt that my four and half years of military service is not enough applicable experience. However, I will be entering a straight 2 year dual degree program at The Maxwell School of Citizenship and Public Affairs at Syracuse University, which consists of a Masters in Public Administration (International Development Emphasis) and a Masters in International Relations (Global Markets and Global Development emphases). After obtaining these degrees, I hope to enter consulting on an international level.

I hope by undertaking this avenue and entering the field of International Development, I will have ample experience to apply to this MBA program. My question now is how old is too old to apply to such a program? Currently I am 28, but after graduate school and some work I will be about 37 years of age. Is this detrimental to an applicant competing against a younger cohort? Also, my undergraduate degree from BYU is Middle Eastern Studies/Arabic with a 3.82 cumulative GPA. Will this type of degree hinder me in the admissions process when I apply? I know this is early in the game for asking these questions, but I feel the need to be prepared, regardless of the timing.

Any advice or feedback that can be given is appreciated.