Big SHMUP hours
Sektori
This isn't a SHMUP but a twin stick shooter, I'm mentioning it first because it's like Geometry Wars both visually and mechanically and everyone played the shit out of that game back in the day. except I wanna' say it's a lot deeper than Gemotry Wars? Not to knock down GW but I don't recall you doing much than shooting and avoiding, this has roguelike/upgrade paths and levels morphing on the fly.

R-Type Delta: HD Boosted
The game itself is excellent even if the package is a little lacking, if you haven't played an R-Type it's a pretty damn hard horizontal (I think I prefer horizontal to vertical actually, sorry Ikaruga) SHMUP where you get a 'Force Ball' which is an attachment that you can put on the front or back of your ship in real time, this can absorb bullets and also fire whatever weapon type you have currently picked up in the direction it's attachedā¦or you can just fir it and let it act as a turret for say, when you need to fire across the top of the screen but move to the bottom. Mastering when to place the force ball in a certain place part of the fun of learning how to play this game.
This is very memorisation heavy and not for everyone, something I feel this HD release doesn't alleviate at all, you get an unskippable intro every time you want to restart from the beginning and there's a practice mode but that's pretty much it. Maybe it's harsh to expect more but based on then ext games I'm about to talk about that have instant retries and/or save states and rewind, it feels like I get better practice on this using an emulator. That said, hasn't stopped me from playing it so maybe your love of the game will negate these issues?
Gradius Orgins
This isn't just one Gradius game it's like 5 but not even that like every game has the EU/NA/JP version and then they have like, unreleased E3 demo versions and then they top it off with a new game completely, Salamander 3, insane value. Gradius is like R-Type except the 'gimmick' this time is the power upsystem, you collect powerups and if you use it it activates the first powerup you have on the list, if you collect another it moves down the list, in this way you choose how you upgrade: do you get two speed asap and then missilies or gun for the laser upgrade? Also like R-Type if you die you lose every upgrade and start midway through a level with fuck all, oof.
As a package this is absolutely amazing, for the price I got it I can't complain at allā¦other than Gradius Gaiden not being here, that's like my favourite Gradius lol. But I can probably spend months just playing Gradius 1 which is all I've tried so far and the game still slaps at that, the fact that this has so many options to help you practice is also more than welcome and really just makes R-Type HD look kind of sloppy in comparison.
G-Darius HD
Another horizontal SHMUP and I would say the 'gimmick' here is you can temporarily capture enemies on the field and depending on what you caught you get different 'upgrades', one enemy can just give you homing lasers, another can act as a shield to shoot through and so on. Also you can choose your route down the Outrun style zone map so there's a lot of replay here providing you can even beat it once. Like Gradius (same team behind the HD port iirc) the options here are impressive, and the presentation might be the best of the bunch here, great stuff.
Astebreed
A SHMUP made just for me it seems, feelsl ike a mechanime if mech anime had long combat scenes every week instead of building up to them. This has quite the control scheme to keep in mind, it's not exactly Radiant Silvergun levels of complexity with the 6 weapon forms at once but you got melee and lock on and basic shooting, and you can combine. Feels like an Armored Core SHMUP or something.