First, you may want to relic characters which you need to relic for current or long-term farming goals. It's not the question "who benefits most" but instead "which hard requirements I need to meet". Of course, if you need to relic several characters then most useful should come first (i.e. for JMK you may want R7 Grievous first and clones last).
Second, you may want to relic characters (or teams) which will help you to complete different game activities (Conquest, assault battles, challenges, TB, etc). Ideally it shouldn't contradict the previous rule.
Looking at the current roster I'd say that GK may be the first goal to make Padme team fully operational.