Look at some of the other posts on travel to the USA, the visa route might not be the best option if you have ever had convictions.

If you don’t wish to study, live or work over there then you can travel on the ESTA see the link below from unlock 

https://hub.unlock.org.uk/knowledgebase/travelling-to-the-usa-the-esta-form-and-moral-turpitude/

the USA does not have access to the police national computer

, if you do plan to live study or work over there in the future then start the visa process now as it can take up to 6 mths 

Hi,

I have a criminal conviction for possession of a class A drug for which I received a fine, this happened around 10-15 years ago and I have not been in trouble before or since that.
 I have provisionally booked a holiday to the USA in December. I understand I cannot enter the USA on an ESTA and need to apply for a B2 tourist visa. I am just wondering if anyone can advise me of when to start the process of applying for the visa?

Thanks in advance.