Seconding Batrider, which is probably my favorite. The million ways to interact with every level make it feel like a pinball machine. Very well structured for having fun while learning, with different courses (including a Boss rush to practice bosses), and the fact that you'll be discovering something new every credit.
I've also mentioned Raiden Fighters 2 and Batsugun Special. The former for it's amazing mega bosses (i.e. stages 3 and 6), the latter for it's immensely satisfying take on the Toaplan cruise'em'up formula without devolving into streaming.
Speaking of Toaplan cruise'em'ups, I love Kyukyoku Tiger and Same! Same! Same!. Both have great Mega Drive ports, with the latter being highly recommended over the Arcade original unless you are a shmup prodigy.
Both games maintain a constant scroll speed with every screen's length or two being like a little puzzle to solve. You don't notice when powered up, but when you die you're taken back to a checkpoint so you'll be forced to really learn and understand the situation to recover. It's never impossible, and always the solution feels so good like "aha!". Then next time when you come through at full power it feels great clinically cutting through everything. Also it's not like when you know it, it's easy. The "solutions" require a lot of controlled movement - tapping, cut backs - mostly the former at full power, but you won't be at full power very often.
Level 6 of Same! Same! Same! is one of my favorite stages in any game:
I made a save state on this level at 0 power and would just play it again and again, initially to practice, but then just because it's so fucking fun.
Kyukyoku Tiger is less intense, and has a far more friendly power up system. But IMO Same! Same! Same!'s power up system is one of those happy accidents in gaming, where even though yes it is annoying to collect the wrong power up, it's also very intense and fun juggling the power up and playing ping pong with it while maintaining focus on dodging bullets and eliminating threats.
Speaking of Toaplan on Mega Drive, Slap Fight MD (the Mega Drive mode, not the port, although the port is good too) is also up there for me. Very much in the same mould as the above except it plays very different depending on your chosen power up strategy. Very fun to experiment with different styles.
Under Defeat is a very different, very modern but just as enjoyable take on the serious salaryman tactical shooter that Same!^3 and Kyukyoku Tiger epitomize. In addition to the difficulty setting and rank, the other difficulty choice you have is which pod you use. Vulcan is the least risky, but scores the least, rocket is super risky, but scores the most, and cannon is in between. Also, the game takes risk vs reward seriously. For highest end stage bonus, you need to complete it with no lives remaining i.e. you're rewarded for living on the edge.
With all these games my advice is, aim for the 1CC, and use your resources!