Set up your assignment reminder rules from the Setup panel by clicking on Reminder rules link.
The rules for sending assignment reminders are followed in priority order, one after the next. Higher-priority rules on the list (lower numbered, higher on the list) get run before the lower-priority rules. If a rule which matches the current situation is found, the actions within it are taken:
Why "none of these"? Let's say you don't want your senior volunteers pestered by reminders (they're always the most reliable, right?) You can define a high-priority rule which matches them by person type or group, has Send reminders set to No reminders, and If this rule applies... un-checked. This has the effect of matching those volunteers, doing nothing to remind them, but allowing other volunteers - which didn't meet these rules - be notified as they match other, later rules.