Here’s the full list of Choose Your Path awards at ball start for each character.
Luke:
Jedi Training
Light Death Star Missions
+5 TIE Fighters
Hyperspace Hurry-Up
Max Time
Light Tatooine Missions
+5% Score
+3X Shot Multiplier
Light Video Mode
Light Endor Missions
Light Escape
+3X Bonus Multipliers
Bonus Held
Leia:
Light Tatooine Missions
Light Death Star Missions
Light Mystery
+3X Bonus Multipliers
Max Time
+5% Score
Jedi Training
Light Endor Missions
Light Hoth Missions
Hyperspace Hurry-Up
Light Escape
+3X Shot Multiplier
Bonus Held
R2-D2:
+3X Shot Multiplier
Light Death Star Missions
Light Tatooine Missions
+3X Bonus Multipliers
Max Time
Light Video Mode
+5% Score
Light Hoth Missions
+5 TIE Fighters
Light Endor Missions
Jedi Training
Bonus Held
Han:
Light Boba Fett Escape
Light Endor Missions
+5 TIE Fighters
Hyperspace Hurry-Up
Max Time
Light Tatooine Missions
Light Video Mode
Light Escape
+5% Score
Light Death Star Missions
Bonus Held
+3X Bonus Multipliers
Jedi Training
+3X Shot Multiplier
The in-game info screen lists the first 10 awards for each character, but more are possible and will appear when enough of the first 10 aren’t available. I tested with the glass off to find those surplus options, by setting up the situation to eliminate everything that could be eliminated, then draining a ball. Doing this when Lightsaber Duel is lit cuts out the most options.
The offered choices are always the top four that are currently applicable (the list is never random.) Examples of unavailable options: can’t light missions or Video Mode when any mission is already running or Lightsaber Duel or Jedi Multiball is lit/running; can’t light a planet or Escape or Video Mode or Hyperspace Hurry-Up when it’s already lit; can’t take TIE Fighters or Hyperspace Hurry-Up when LSD/Jedi is lit/running; can’t take Jedi Training after that is maxed. The following four awards are always available and will comprise the list if all other options are eliminated: +3X Shot Multiplier, +3X Bonus Multipliers, +5% Score, Bonus Held.
Max Time is offered only during Lightsaber Duel and only affects that timer. Light Escape means the outlane (not Boba Fett.) Light Boba Fett Escape doesn’t light or start the mode directly; it lights all shots white but they follow standard rules for progressing to EFBF from there (if you then enter a mission and shoot the shots that were white, they will unlight without progressing.)
Jedi Training can appear for R2-D2 and Han. It’s very far down, such that it’s only possible while Lightsaber Duel is lit or running. If you drain then, you may want to take it since it won’t be available otherwise. Or even intentionally drain for it if you need it badly enough!
Bonus Held is also very far down the list for all characters. For everyone but Han, it can only ever be available when Lightsaber Duel is lit but not running - that’s the only time that both +5 TIE Fighters and Max Time can both be off the list to open a slot. Han can see Bonus Held repeatedly by draining during LSD, and choosing it repeatedly can compound your bonus quite a lot. I once unintentionally did this, draining three times during LSD with Han; the repeated bonus-holding compounded to over 2 billion!