If I use Welder and attach a Fire Energy to an Eevee that has the "Energy Evolution" Ability, do I draw the cards for Welder first or search for a Flareon due to "Energy Evolution" first (or is it a choice)?
Since they are simultaneous actions, it is the player's choice of which order they can do this.
Source: TPCi Rules Team (2019-05-09)

Relevant cards

Note: All applicable cards may not be listed below.
SM10_189
SM10_189
SM10_189A
SM10_189A
SM10_214
SM10_214