Quoted from vikingerik:

This isn't remotely close to true. The way you blow up AIQ is to get to the wizard modes. Battle Royale, Battle Thanos, Super Victory Laps, Computer Frenzy, and Trophy Mania each score 200-400 million and total 2+ billion all together. If you don't reach them, you'll top out at a few hundred million from a handful of quests and regular multiballs, no matter what you do with any gems.

Have you tried reading the screen? The game displays it each and every time you level up an avenger.
Hulk level 1: double Hulk Rampage scores.
Iron Man level 1: double Arc Reactor scores.
Captain America level 1: double Shield Bonus.
Black Widow level 1: Thor inlane helper (2x progress for hitting Thor after the left inlane).
Thor level 1: Super Slings.
Black Panther level 1: Longer combo timers.
Level 2 avengers all double all scoring at their shot, except Iron Man, he doubles all of Iron Man Multiball.

Free hits help you complete anything that you use them for. It's up to you strategically whether you want to do it on Soul Gem, or another gem quest, or something else like say Iron Man jackpots or Binary hurryups.

The Super modes are awards from completing a line on the computer grid. It's the first info screen, hold a flipper for three seconds and you'll see what's on which line. (And they don't score all that much, 20 million is a good run on any.)

The game tells you, on the screen, each and every time you hit the Captain Marvel shot, how many more shots (premium) / spins (pro) for the next Binary hurryup.