Doubtless you will be distressed to read that you have been convicted and have a criminal record.
However whilst this may seem life changing it rarely is.
Convictions for minor railway ticketing offences are at the lower end of the scale of convictions.
It may appear on an enhanced DBS check (opinions on the forum vary as to if, when and for how long convictions stay on a check).
Actions for you to take:
1. If you have not already done so pay the fine and associated costs immediately. This is to prevent matters escalating.
2. Check your contract of employment to see if you are required to declare any conviction to your employer.
3. Are you in a regulated profession or occupation which requires you to declare convictions?
4. If the answer to (3) and / or (4) is YES are you a member of a trade union TU or professional association PA who can give you advice as to how to declare your conviction to your employer and regulator?
5. If the answer to (4) is yes contact them immediately. Some regulators require convictions to be disclosed within a very short period of time so you must make sure you comply with the deadline hence getting TU or PA advice immediately is essential. Failure to declare is almost always seen by a regulator as an aggravating factor and can be the "tipping point" between the Regulator issuing a warning or taking more drastic action (ie issuing strike off or suspension proceedings).
6. Do not worry about the VISA issue at this time as it is not a live concern. Take professional advice at the appropriate time. NB
@Fermiboson point that visa and immigration advice can only be given by a qualified specialist.
7. Finally TfL nearly always take ticketing matters to court (rather than offering out of court settlements ) so it is unlikely that you would have avoided the court summons even if you had taken advice from a solicitor.