Influence of Spouse's nationality and my length of citizenship for getting a Secret Clearance?

1. My spouse is living with me. She is a greencard holder (legal US Permanent Resident) but a citizen of Bangladesh.
2. My parents are not US resident, they are citizens of Bangladesh and residing over there.
3. I am a US Citizen and became a US citizen 2 months back.

I heard a few cases where Top Secret clearance was denied because of a foreign national spouse. But have not heard any case regarding Secret Clearance. I also heard that if I have not been a US Citizen for at least 1 year, the clearance is not given.

I am about to get a job offer that requires Secret Clearance (not Top Secret). Can anyone (preferably an investigator) tell me whether the above conditions will be a problem for me to get a Secret Clearance?