Looking back at my terrifying trip, I would rather have visited ancient Rome than the Jurassic period; running from a T-Rex is exhausting! Next time, I had better pack some comfortable running shoes just in case.

To express a preference about an event that already happened in the past, we use "would rather have + past participle" (would rather have visited).

"Had better" is always followed by the bare infinitive (pack) without "to".