If I could only have 3 "shmup consoles" they would be:
1. PCE
2. Saturn
3. PS2
The PCE is the best due to its arcade ports AND exculsive shmups. Next comes the Saturn with all those great arcade shooters from the '90's. It totally lacks any real exclusive shmups though. Finally the PS2 is the system to have for your modern day manic bullet hell arcade shmups.
I like the Dreamcast, but its shooter library is vastly overated. Most of the better shooters on Dreamcast have superior versions on other consoles. Also it completely lacks games made by Cave, which is sadly the only really good shooter developer left these days.
The Dreamcast, Genesis, NeoGeo, and PS1 all have some great shooters on them, but they are greatly outclassed by a PCE-Sat-PS2 combo. The Windows PC is also home to some great exclusive shmups such as the "Touho" series (
www.shrinemaiden.org).