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Get a BS in engineering. As long as the school's engineering degree is ABET accredited, it doesn't matter at all which school you choose. There is no advantage picking an Ivy League over a state school - save your money. In fact, your best bet is probably Texas A&M.
Don't waste your time with an MS in engineering. It is a fairly useless degree. They'd give you credit for a year of experience and a couple grand extra. Let the company that hires you to pay for your grad school.
If you want to be a civil servant, you will need to get a co-op position at NASA while you are in college. NASA has very few openings and almost all of them are reserved for co-ops.
If you can't get a coop position, apply for engineering positions with one of the contractors that support NASA. You'll be doing the same job, just with a different badge. Most of the flight controllers for the ISS aren't NASA employees, they actually work for United Space Alliance (USA). At almost every NASA centre, many of the people work for USA, Boeing, Lockheed, Raytheon, Hamilton, and other companies.
Now, if you really want to be a research scientist, I don't know much about their entry path.

Amity Global Business School carries forward Amity's vision of bringing quality education to talented youngsters living in different parts of the country and giving them professional education that matches with the best world has to offer.
Amity Global Business School Campuses in 15 cities are an embodiment of a dream to establish world-class institutions which will groom young future leaders across the country.YES Their degree is valid in Ahmedabad, Bangalore, Bhubaneswar, Chandigarh, Hyderabad, Indore, Kolkata, Mumbai, Noida, Chennai, Cochin, Patna and Pune. In London and Singapore, AGBS is preparing leaders who shall shape the global economy.

Candidates who desire to join the postgraduate course in physics must have a graduate degree. They must have secured above 55 percent marks in their final exams. A relaxation of 5 percent is available in the case of students of the reserved categories.
Higher study options after B.Sc Physics
Given below are some of the higher studies options that the students can choose from.
B.Ed
B.Tech Electronics
M. Sc Acoustics
M. Sc Applied Electronics
M. Sc Astronomy
M. Sc Astrophysics
M. Sc Electronics
M. Sc Geophysics
M. Sc Medical Physics
M. Sc Nuclear physics
M. Sc Physics
M. Sc Physics
M. Sc Vacuum Sciences
Master in Atomic and Molecular Physics
Masters Degree Physics
MBA
MCA
PG Diploma in Physics
Postgraduate Certificate and Diplomas Physics
Postgraduate Certificate in Education Physics