NES/Famicom - A lot of the classics are here many are very affordable, Complie, Konami and Hudson are well represented. Recca was one of the first Danmaku.
Master System- not much outside of R-type and Aleste.
Genesis/Mega Drive- SO much good, most of them are affordable or have easily found repros. Thunderforce, Eleminate down, Glaylancer, Darius 2, countless others. Probably the best platform for people not looking for Danmaku.
SNES/Super Famicom- Not my go to for shmups, but Axelay and Cotton 100% get play quite often.
PC Engine- Good for shmups, but they get pretty samey after awhile. I think it's a bit overrated in my opinion outside the Star Soldier games.
PS1- A little bit of everything, I don't like the Cave ports, but there was A TON and if you have a Japanese System MOST are affordable.
Saturn- Probably the holy grail system for Shmuppers, but it's also way too expensive to collect for and disc rot happens on this more than other platforms. I think the Holy grail game Radient Silvergun is a bit overrated. It's my favorite Console of all time. But I'm going to need a Psuedo cart to play burns on. I prefer the Dodonpachi on Saturn over PS1.
N64- *video of Iori Yagami laughing*
Dreamcast- Same problem the PC Engine has, there are a lot of Shmups on it, but they get pretty samey and they get pretty expensive. That Said, I really like Psyvarar 2 and Karous. The Latter doesn't seem to burn well.
PS2- Like the PS1 a bit of every kind, Every company is represented Some of Cave's best is here. Gradius 5, R-Type Final, If you import some Psikyo games (BUT there's a better platform for Psikyo games) But it's overlooked as a Shmup machine. THUNDER FORCE VI and it has a pretty good Megasis Emulator.
XBOX- Modded system there are a handful of Good Shmups like Shikigami no Shiro 2 and Psyvarar.
Gamecube- Only a few shmups here plus whatever the gameboy offered. It won't be your primary.
Wii- Same as the Gamecube, there's some goodies but nothing mindblowing.
PS3- It's not the 360, but It's the only way to play Ketsui on a console with no hassle.
XBOX 360- Everyone's favorite modern Shmup machine even though it's region locked and getting around said region lock is a pain. Heaven if your style is Danmaku.
PS4- Quite a few gems on here
XBOX ONE- *crickets* Most of the 360 goodies aren't BC.
Swtich- Probably the best Nintendo system for Shmups...if you don't mind that most of them are digital only. Psikyo is there, Some good indies, Ikaruga is there A Psyvarar is coming, It just needs some Cave games an it's the best ever.
PC with MAME- If it's not Switch it's a PC with MAME Best way to play arcade games, alot of good stuff on STEAM. This is probably where I will do 98% of my Shmupping.
Got anything to add?