Games

I like Xevious and Zaxxon. Zaxxon was cool because it had a unique isometric perspective that I haven't seen in another game.

Gradius 3 specifically I found to be quite fun. Its too bad Konami retired the Gradius series, but I suppose its probably better that way.

The Panzer Dragoon series is a great arcade shooter series.

Contra. Contra 4 specifically on the Nintendo DS I felt had the perfect balance. I really liked that entry.

Run n’ guns: Contra III: Alien Wars and Pocky & Rocky

Smups: Space Megaforce

• Contra: Hard Corps(Sega Genesis) is an old side scrolling shooter, has local co-op.
• Cuphead(PC) is an old school side scrolling shooter, has local co-op.
• Enter the Gungeon(PC) is a top down roguelike shoot em up, has local co-op.
• Furi(PC) is a top down boss fighting game.
• Gauntlet reboot(PC) is the adaptation of an old franchise, has 4p local co-op.
• Geometry wars(PC) is a shoot em up series.
• Mega Man Zero(GBA) is a side scrolling platformer series.
• Risk of Rain(PC) is a roguelike shoot em up series, has local co-op.
• Touhou Project(PC) has a bunch of games like Gunbird in the series.
• Vampire Survivors(PC) is a top down shoot em up, has local co-op.

Shmups, I'm only a beginner but I have a few suggestions:

• ESP Ra.De. - somewhat slower bullet hell with pretty interesting scoring, the "Psi" re-release has a lot of useful QoL features.
• Espgaluda II - you could think of it as a successor to the former, it has refined gameplay and recent releases have great QoL features. Somewhat faster paced bullet hell?
• Ikaruga / Radiant Silvergun - Although these are two very different games, they have entirely different mechanisms to most other shmups. Ikaruga feels like a "puzzle" game a lot of the time, while Radiant Silvergun has some light RPG elements. Both are somewhat hard to get into imo.
• Dodonpachi Resurrection - great starting point re bullet hells, the recent re-release offers a ton of QoL features and the game itself has interesting scoring / gameplay. Soundtrack is awesome.
• Raiden IV - Super biased, but I love the soundstrack. Pretty great, if simple, game otherwise.

I have many more shmups in my backlog (Ketsui, Dodonpachi Daioujou, Battle Garegga, Rolling Gunner, etc) which I'm sure I could recommend, but seeing as I haven't played them first hand yet... I'll leave it there for now.

How about autoscrolling shmups where you don't die after every hit and get to upgrade your ship between missions?

The oldschool entry in this niche would be Tyrian – released in 1995, made freeware in 2004, then ported to modern OSes.

2004 was also when Jets'N'Guns came out. It looks more modern, has a quirky sense of humor and a badass metal soundtrack. It also has a sequel.

Both games can be found on your (PC) digital marketplace of choice.

Shmup: R-Type Delta, but you really can’t go wrong with any of them.

Run ‘n Gun: Gunstar Heroes, love the weapon power up system and its co-op.

I played the fuck out of Cannon Spike on Dreamcast

https://en.wikipedia.org/wiki/Cannon_Spike

But I was a huge SmashTV fan back in teh day. I still play it when I see a cabinet.

I tried to get into the mindset to get good at Ikaruga but I just cannot invest that kinda time.

Dreamcast had so many good shmups.

Guardian Legends and 1942.

Some more modern run and guns - Blazing Chrome and Huntdown. Both of those are a good time.

Sunset Riders is a great run and gun.

I really like Gunlocked, which is a more short-form and arcadey roguelite shmup