A police caution is not a conviction but an acceptance of guilt to a minor offence by you. Technically, it is recorded should you offend in the future.
A visa waiver form asks if you have ever been convicted of a crime of moral turpitide which is anything from theft and minor assault to murder - all of which require intent on your part.
If you have ben convicted, you should mark the box on the visa waiver as yes then you will get interogated by an Immigration officer.
The advice given by the US embassy in relation to applying for a visa for a criminal convictions is a blanket piece of advice to prevent delays once you are in the US . If these are admitted on entry, the DoHS officer has to make enquiry into the admission, which is a lengthy process to ensure that entry should not be refused and that you meet the exceptions to refusal. Hence the Embassy prefer you to go there and geta visa as they do all the checks beforehand.
The law comes from the -
Immigration and Nationality Act, 8 U.S.C. 1001 Section 212 c (A) i 1 and the exceptions to are -
For drugs related offences - no entry, never ever if you admit dealing / trafficking not simple possession or none of our pop stars would ever get in.
For moral turpitude the exceptions are -
1. If the crime was committed when you were under 18 and 5 or more years before trying to enter the US.
2. If over 18, the maximum sentence was 1 year and you were sentenced to 6 months or less.
So, the bottom line is this. You are exempt from requiring a visa as you were never convicted of anything, tick the box on the visa waiver form where it asks if you have ever been convicted of a crime of moral turpitude as 'no'.