I say (my way is more fun...and progresses from "universally appealing" to "niche audience"):
UNIVERSALLY APPEALING (easy):
Lords of Thunder...it has the biggest aesthetic "wow" factor. It is truly unique in its visual presentation. It is a lot of fun to play...even for casual shooter fans. A lot of people are telling you to buy the "best" game first...but I think you should go for the best visual treat first (don't worry, the game itself is solid). Then...
CASUAL SHOOTER FAN (easy):
Gate of Thunder: a fantastic game with a more "mainstream" (for shooters) aesthetic. Probably a stronger game than Lords (I have argued as much in the past), but it can't quite match the fantasy theme of Lords (the atmosphere).
GRADIUS FAN:
Gradius II is a great game (again, I posted about the game years ago), but I would say that it is for Gradius fans. You know what you are getting here. Haters are gonna hate (they are WRONG...the Gradius series DOES allow you to recover from setbacks and/or checkpoints, even if you are reduced to a pea-shooter). I raved about Gradius II when I first got it for the PCE years ago...and I haven't really changed my mind.
MANY PEOPLE PLAY SHOOTERS THE WRONG f*ckING WAY:
You should never turn off the console because you died and lost your powerups.
The entire point of the goddamn genre is to figure out a way to SURVIVE, even with a pea-shooter.
Use continues when you a learning a new game (or trying to beat a challenging game), because you have to practice, and you have to experiment with different strategies for survival.
You want a repertoire of survival skills, NOT A "PERFECT PLAYTHROUGH"
A *perfect* PLAY-THROUGH can be the final product after lots and lots of *organic* practice, experimentation, and pure desperation.
But your games should always have *some* spontaneity (even if *you* have to initiate it...for example: by not playing the exact same way every time)
/rant