Answer:
Either! My trick to figure out which way you should say it is to say it without "Jon". Whichever is the correct way to say it without Jon is also the correct way to say it with Jon.
For example:
Incorrect: Me went to the store.
Correct: I went to the store.
That means you would word it: Jon and I went to the store.
Incorrect: She threw a snowball at I.
Correct: She threw a snowball at me.
That means you would word it: She threw a snowball at Jon and me.