Gee

I have my interview in London coming up very shortly. My wife is being sponsored for a Green Card for a job in the US. Hopefully we will shortly be going there with our two kids. However, I am worried. I have convictions on my Police Certificate from 16 years ago and am not sure how I am going to handle it.
Could anyone give me an idea as to what I should expect at the interview? Is it as scary as I believe it might be?
I should qualify for a waver considering the nature of these old offences. However, I am expecting the worst. Would appreciate a reply or even advice.