Сопоставим правила использования инфинитива (To-infinitive), голой формы инфинитива (Bare Infinitive) и герундия (Gerund) с их примерами.
To-infinitive:
Bare infinitive:
Gerund:
Ответ:
To-infinitive: after would like / would prefer / would love (to express specific preference), to express purpose.
Bare infinitive: after modal verbs (can, may, must, should, etc.), after had better и would rather.
Gerund: as a noun, after happy, glad, sad, in combination with the verbs spend, waste, lose (time, money, etc.), in fixed expressions: to tell you the truth, to be honest, to sum up, to begin with, after go (for activities), after love, like, enjoy, prefer, dislike, hate to express general preference.