Academic Writing: Numbered points in text etiquette
They're both acceptable, nobody except very careful English fanatics are likely to care, but the latter is preferable. Reasons:

Periods are more &quot;final&quot;. They indicate the end of the sentence. That implies that you should instead use capital letters if you stick with periods:

The loser will: 1. Get laughed at, 2. Pay for drinks and 3. Have to run outside naked.


Because periods indicate the end of the sentence, one doesn't expect to see multiple periods in a single sentence. Using ) avoids this problem.


As for whether or not to use a semicolon, again it's up to you, but the comma is fine here. That's because the three things listed are all pretty related, short phrases, and on an equal footing. Semicolons are better when a sentence is complex or has other punctuation symbols. Example of something where I'd prefer the semicolon:

This new year, I resolve to: 1) cook 100 breakfasts for my wife - she deserves it; 2) set tests such that 50% of the class fails to shake my reputation as an academic Santa Claus; and 3) run for president.