Weird take, but Tyrian 2000. Easy to get into. Lot's of menuing though.
Oh, it's also free on GoG.com. D'oh, forgot to mention that.
The Guardian Legend would work, its a hybrid of a shmup and overhead adventure game. That also happens to be one of my favorites. :) Just to note that shmups are rarely ever speedrun material because the majority of them are autoscrollers but technically can be ran. I love shmups but I don't speedrun them personally I 1cc them and no deaths.
If you're including platform shooters or run and gun games I can recommend Mercs (Genesis) and Flimbo's Quest (C64), both of which are fully optimised and under 20 minutes!
Neptunia Shooter. Short (under 9 minutes), very forgiving compared to other shmups, and it even has a speedrun leaderboard in-game!
gunforce for the arcade or trick trap would make great speedruns although trick trap is more of a maze game. I did a run of it on my youtube channel along with gunforce 2.