Racketboy

Game Boy Advance SP:

Super Mario Advance Series (Good to have classic Mario games on the go.)
Metroid Fusion
Mario Kart Super Circuit
Mario Pinball Land
River City Ransom EX (A higher quality port of the NES version.)
Metroid Zero Mission (Fusion is obsolete, but this is still a great game.)
Golden Sun Series
Sonic Advance Series (Like the older Sonic games, but portable.)
Crash Bandicoot: The Huge Adventure/N-Tranced (It's Crash in 2D. Very fun games.)

Yes - a saturn is the way to go if you want to experience some top notch shooters. My personal favourite is soukyugurentai which has some great visuals and game play. Suffice to say I am not very good at shmups so I have not managed to complete it but what I have played I have enjoyed immensely. It is also one of the more reasonably priced games and regularly appears on a certain auction web site...

Sega Saturn is pretty much the king of 2D shmups ported from arcade. Most are arcade perfect, some show slight differences but are still damned fun.

Check out Retro Core's Saturn Shmup special:
http://www.segagagadomain.com/retro_core__info-sss.htm

3 hours and 22 minutes of shmups reviews on Saturn.

And yes, it's quite expensive. You can "try before you buy" via MAME for may titles.

And if it's still too expensive, have a look at Megadrive/Genesis titles. Plenty of good shooters on that platform that are quite cheap.

Aleste GG and Power Strike II for Game Gear. Not sure how easy they are to find. IMO the only shmups worth playing for that system.

IBARA for PS2 is my favorite shmup of all time, and I own almost all shmups for PS2 and Saturn. I play it at least once a week. I am trying to beat it without continuing. Once its sequel, Pink Sweets, is released on the 360...I am all over it.