So... which classic shmups should I play next?

[BPzeBanshee]

Raiden series is awesome, but it may make you cry.

RII is better than the original, but DX is better than RII.

I agree. Go for the Raiden series.
Great games, classic gameplay, and classic difficulty.

Plus, you can transition onto the newer 3D Raiden III and IV later if you so choose. III was ok, but IV is much better.

This, this, and this.

[Drum]

Dragon Breed/X-Multiply, Galaga, Asteroids.

[kevenz]

-1944 by Raizing, it's not very old but it's one of my favorite.
-Raiden Fighters 2, same as the above, badass shooter with crazy techno music.
-Batsugun, it's basically the first Cave game!
-Truxton 2, challenging but really fun.
-X-Multiply, another challenging one but it's very unique with the two arms you have that serve as a shield.

[Deca]

I have to warn that your mileage may vary drastically on 1944. I'd rather put a needle through my eye than play that game again after STGT, but a lot of people seem to love it for some reason. I can vouch for Raiden Fighters 2 being cool but that's also late 90s. Batsugun, special in particular, is fucking awesome.

[burgerkingdiamond]

I majorly second Twinbee and Gemini Wing.

I would kill for a Gemini Wing pcb, but I've never even seen one pop up.

[Aquas]

Some I like are Dragon Spirit, Star Force, Flying / Fire Shark, TwinBee and Gradius.

TwinBee 1 has awesome gameplay and crazy rank that kicks in on the later stages. Almost feels like a bullet hell at times.

[Hagane]

Omega Fighter, Gunbird, Raiden DX, Gokujou Parodius, Shippu Mahou Daisakusen.