If you're looking to get into Cotton, play the other games. If you're looking into the shmup genre as a whole, play some of Cotton's games and some other stuff.
For the record, I'm very glad Rainbow Cotton got a re-release and localized outside of Japan. There was clearly a lot of love put into preserving it's presentation, adding a ton of QoL features, and using the english fan translation as a basis for this localization to make this the best version of Rainbow Cotton. But unfortunately you can only fix so much.
This remake did what it can to make this far more palatable to play, but Rainbow Cotton's inherent design is still an issue. Stages go from having some consistent fun to being extremely claustrophobic, enemy and boss patterns being extremely slapdash, and Cotton's player model being far too big to see whats ahead/in front of you (which this remake did fix a bit by readjusting the camera, but its still annoying to deal with).
As much as I respect the developers for making this game available on modern platforms, there's better games out there to sink your teeth into.