The correct answer is the first option, "Would you like to play baseball, or would you prefer to swim?"
This option is correct because it correctly makes use of a comma (,) and question tag (?) as follows:
i) The comma indicates a pause between the clauses "would you like to play baseball" and "would you prefer to swim".
ii) A question tag is used at the end of a sentence that is asking a question. Sentences that start with "would you", "can they", "will he", etc., need to end with a question mark (?) to be punctuated correctly.