Mastery Upgrades

Mastery Tokens can be spent on four upgrades (blue up-arrow at the top left corner of the barrels list). They are both unlocked with the Barrel Mastery. They all have the same costs. The last one, which increases the v4's boost, is unlocked at x500 Stars and requires the previous upgrade on Level 1 or higher.

More Magnets
Focus on this one first. Its boost is massive.

More Golden Scrap
The second worst one currently. A must have if you plan on getting tons of Golden Scrap; if you don't plan on farming soon you should get the other ones first.

More Tires
The second best one right now, it can double the tire gain speed. Very useful, as leveling the v5 is much faster then.

More Wrenches
Well, more wrenches, more v4 levels?

Better Boost
Can give hundreds of brick levels. Very good for getting more progress on stars.

Better Rewards
More magnets from the weekly team leagues, why not? You should ignore it if your team only gets the very small league rewards.

More Fragments
By far the worst one, as fragments are nearly useless.

More Steel Beams
The third best currently, as it doubles your beam gain.

More Scrap
Not great, but not bad. Can make prestiging / reaching new barrels easier and stars cheaper.

More Tokens
A nice upgrade, definitely worth the tokens as it doubles your Combine Token income.

Faster Level Up
The fourth best one currently, as it makes you able to level up way faster, which gives you two benefits at the same time:
 * More Bricks by resetting the level
 * More Magnets (~30% more)

It used to require x1000 stars until the release of the v6, now it is unlocked at x1200 stars.