The ideal solution for you would be to proceed further for higher studies in engineering, if you have an interest and appititude for the same. A good GATE score must help you get into a good MTech or ME programme, and with the rise in the number of engineering colleges,  a teaching position will not be too difficult to find.

With about three years of no work experience, cracking the job market may be slightly difficult. Even cracking  a good MBA programme would also be not very easy because good colleges would not look tood kindly to you not working for the last few years.