If you roll on 2 or more items, and let's assume you have the highest roll for all of them, you'll get whichever resolves first. So, whichever one the other 7 people roll on or pass first, that's what you get.

Once you get the one item that resolves first, everything else essentially becomes a "pass" roll.

In your example, to ensure the ring is preferred, roll on the ring but do not roll on the body. When the ring resolves, if you do not win the ring, then roll on the body.