Here is the Order of Operations from the Glossary:
There are two types of special abilities that define how a special ability is carried out: Ongoing Abilities and Instant Abilities. When a single card has more than one special ability (including gained abilities), and an order is not specified, perform the abilities in this order:
• First, complete all special abilities in the order written on the card except those that add a character to the battle (banding abilities). Note that some special abilities can happen together even though they may be separated by a period (e.g., Authority of Christ promo). Second, if the card is a character with either a gained ability or a weapon-class enhancement, then activate the gained abilities in the order gained. Finally, activate the special abilities on the carried weapon-class enhancement.
• Complete banding abilities.
• Complete any Choose Blocker or Rescuer abilities.
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I say the side battle comes first, since it is printed on the card. The "play first" is treated as a "gained ability" (for the purpose of this order).