Scoring mechanics started to evolve as soon as chains and combos became common (In that respect I would start with Galaga), later followed by complex bullet patterns.
Another aspect which I would seriously consider are power up mechanics, which often identifies the gameplay more than scoring and is usually tied with it.
Here there are some notable games in relation to original mechanics and scoring.
Mechanics:
Gemini Wings (you collect smart bombs as tails and you can release them in a stack order)
Ikaruga (you can switch between two shooting colors, and you can only destroy enemies of the respective tint)
X-Out (you can change your weapons between stages, and the configuration is truly important... later games in the same genre are Stargunner and Jets 'n' Guns)
Xenon 2 (weapons can be took during levels or later in a store, the configuration is important)
Alpha Mission, Terra Cresta, Action Fighter, Xevious, Twin Bee (you can attack land units with an alternative weapon)
Gradius (each power up fills a bar with weapons to choose from)
1943, Twin Bee (when you shoot a power up it changes to a different one; same idea was used in Platypus)
R-Type (the ship itself isn't very powerful, but you have a companion drone which can be detached and powered during the game)
Mechanics/Scoring:
Do Don Pachi (bullet hell, plus chains which influence the multiplier score)
Space Invaders Extreme (hitting enemies in rows/columns/etc. raises the multiplier)
Rayforce, Raystorm, Raycrisis (you can lock enemies and then unleash your energy missiles: if you lock and destroy entire formations you are awarded bonuses)
Twinkle Star Sprites (a versus shoot'em up: the bigger the chain, higher the chaos you send to your adversary)
Scoring:
Zanac X Zanac (chains which influence the multiplier score)
Mutant Storm (each enemy destroyed fills up a multiplier bar, so that subsequent enemies give you more points thus making easier to reach extra lives and higher records)
This website could be helpful as a reference:
http://shootthecore.moonpod.com/articles.php
Another aspect which I would seriously consider are power up mechanics, which often identifies the gameplay more than scoring and is usually tied with it.
Here there are some notable games in relation to original mechanics and scoring.
Mechanics:
Gemini Wings (you collect smart bombs as tails and you can release them in a stack order)
Ikaruga (you can switch between two shooting colors, and you can only destroy enemies of the respective tint)
X-Out (you can change your weapons between stages, and the configuration is truly important... later games in the same genre are Stargunner and Jets 'n' Guns)
Xenon 2 (weapons can be took during levels or later in a store, the configuration is important)
Alpha Mission, Terra Cresta, Action Fighter, Xevious, Twin Bee (you can attack land units with an alternative weapon)
Gradius (each power up fills a bar with weapons to choose from)
1943, Twin Bee (when you shoot a power up it changes to a different one; same idea was used in Platypus)
R-Type (the ship itself isn't very powerful, but you have a companion drone which can be detached and powered during the game)
Mechanics/Scoring:
Do Don Pachi (bullet hell, plus chains which influence the multiplier score)
Space Invaders Extreme (hitting enemies in rows/columns/etc. raises the multiplier)
Rayforce, Raystorm, Raycrisis (you can lock enemies and then unleash your energy missiles: if you lock and destroy entire formations you are awarded bonuses)
Twinkle Star Sprites (a versus shoot'em up: the bigger the chain, higher the chaos you send to your adversary)
Scoring:
Zanac X Zanac (chains which influence the multiplier score)
Mutant Storm (each enemy destroyed fills up a multiplier bar, so that subsequent enemies give you more points thus making easier to reach extra lives and higher records)
This website could be helpful as a reference:
http://shootthecore.moonpod.com/articles.php