I see! Sorry I thought people had experience here. I'm really unsure what to do to be honest
From what you've said about your conviction/caution, If you follow the rules you need to apply for a tourist visa - no exceptions.
However, I read that CBP are currently reviewing applications from UK citizens with cautions, because they're unsure how to treat them, (it's not technically a conviction, but you are basically admitting to committing a crime) this is resulting in severe delays for people with cautions making visa applications (I've heard as long as a year)
You have two choices;
Apply for a VISA - wait as long as a year and probably get denied (recent caution for fraud with previous convictions, all CIMT)
Tick "NO" to the ESTA online form, (I almost guarantee it'll come back as approved) put on your poker face and go through customs, unless there's more to your history, or something you're not telling us - I'm 99% sure you'd get through. (I know people who've done serious jail time who walk through on a regular basis..)
Also, bear in mind - if you apply for a VISA and it's denied, then there's no chance of an ESTA (it'll auto-deny you based on your passport number/name/DOB)
*Bear in mind, if you tick "NO" and in the unlikely event you're found out - prepare to bear the consequences*