Edit: This post excludes the 16-bit consoles.
If anyone is looking for one console for shmups and one console only that offers a ton of quality shooters, I don't know why anyone would recommend anything other than a Japanese 360. All of the Saturn and Dreamcast recommendations are almost pointless unless you like the novelty of the old hardware or are after a few select games. It's really getting to be a tired argument.
The 360 not only has some of Dreamcast's and Saturn's most popular shmups restored in HD and with a cheaper price tag, but many games from Cave, G. Rev, Konami, Raiden series, etc. Everything from colorful bullet hell's, a plethora of vertical and horizontal shooters, cheap indie games, various exclusives, and old-school-style shmups such as the Shooting Love collections and Raiden Fighters.
I mean, the Sakura Flamingo Archives alone has several Dreamcast games on the same disc for less than $60 along with Ikaruga on XBLA, a re-release of Under Defeat, Shikigami No Shiro III and some nice restored Saturn STG's on XBLA such as Raystorm and Radiant Silvergun.
