1/3 HP minimum. 1/2 HP if you want to sleep through the night.
Heavy rain means water piles up fast. A tiny 1/6 HP or 1/4 HP pump will struggle to keep up and might trip or burn out right when you need it most. Go with a 1/3 HP pump rated for at least 2,000 gallons per hour.
If your cover is huge (over 20x40) or you deal with tropical downpours, step up to 1/2 HP. The extra cost is maybe $30–40. That’s cheap compared to a torn cover or a flooded yard.
Don’t waste money on a “heavy duty” label. Check the GPH rating at the head height your pump actually sees (most people run it through a hose, not perfectly flat). And get an automatic pump with a float switch — you don’t want to stand out in a thunderstorm to turn it on.
Future You: dry, happy, and not cursing your impulse buy at 3 AM.