Answer:
It was a rainy day but, Joan and I had planned a trip. Joan wanted to go to the beach for a swim. I wasn't sure if we should go.
"I think we should wait a little longer, at least until the rain shows some signs of slowing down," I suggested.
"We can't swim without getting wet anyway," replied Joan, questioning my choice of swimsuit, the one my mom had bought at a secondhand store.
Explanation:
The best option to complete the parts where punctuation is missing is a comma.
1. It was a rainy day, but Joan and I had... --> commas are placed before the conjunction joining two independent clauses, as is the case here.
2. "I think we should wait a little longer, at least until... --> this type of usage is commonly justified as avoiding confusion. The way we read the sentence without the comma changes, and can cause confusion.
3. questioning my choice of swimsuit, the one my mom had bought... --> commas are used before phrases or clauses that somehow offer an explanation or further information about something previously mentioned. In this case, the speaker is offering further information about the swimsuit.
Note: For case 3, I believe a dash is also an option, since it can come before an explanation or further information as well. Still, a comma is usually preferred.