Just a normal day. Come home from work. Put the kettle on. Feed the dragon.
"I had better" is an English idiom, meaning "I must". The word "had" has nothing to do with the past.
This construction implies a certain amount of compulsion.
Literally :- "It is better FOR me to feed the dragon"..........otherwise watch out damsels.....
The closest analogy in English is 'I had better.....'
To say 'I prefer' we use the slightly different expression in Welsh
'Mae'n well gyda fi (gen i in NW)' = I prefer (literally 'It is better WITH me.......)
Mae'n well gyda fi fwydo'r ddraig na'r ci = I prefer to feed the dragon (rather) than the dog.