You were issued with a fixed penalty notice. To quote directly from the Home Office website: "Penalty notices are not the same as criminal convictions". So you can lawfully state that you've never been convicted of a criminal offence. Source:
http://www.homeoffice.gov.uk/anti-social-behaviour/penalties/penalty-notices/
An enhanced CRB check will automatically contain all of the same information that a standard check does. See here:
http://tinyurl.com/yb9wckr
Additionally it can show any any information deemed to be relevant by a senior police officer (or other relevant source). For example it can show offences committed by a subject's partner or family members. (I know of a teacher who found that offences committed by her husband appeared on her CRB check). It can also show unsubstantiated allegations against the subject. (A teacher posted, here on AB, when he found that his CRB check included an allegation of sexual 'grooming' made against him, even though he'd never been questioned or even told about the allegation).
It's probably unlikely, but not impossible, that your FPN would show up. Even if it did you wouldn't automatically be barred from entering the teaching profession.
Chris