I plan to attend Rosh HaShanah and Yom Kippur services this year for the first time. Will I be expected to donate money during the service, like in a church service? If so, what’s the "right” amount?
You will not be expected to give money during the Rosh HaShanah or Yom Kippur services. In fact, it is customary to not exchange money on Shabbat or major Jewish holidays.