A little side scrolling shoot'em up that I've been playing recently is
Toon Shooters 2: The Freelancers. Very much free-to-play, no overwhelming grind, nice aesthetic, and easy controls. No timers, no stamina, no ads (except for freebies), play as much as you want to when you want to. I have no idea how they'll make their money. Which I'm fine with.
The main selling points of it are nice cartoonish graphics and online (cross-platform) multiplayer. Android/iOS/PS4 I think. It's got five or six "characters" to choose from, each with a different weapon loadout and super-bomb-thing. You power up your character's main stats (permanently) before the level through collected cash, and "P" pods give you bigger/better attacks throughout the level, so it's pretty standard fare. You can choose two weapon side-pods/wingmen, allowing you to vary a character up a bit, but you only get to use them after collecting the 2nd and 5th "P" pod. Two lock-on missile pods tend to be a good "take anywhere" option, but there's a fair few thingies to choose from and try out.
So far it's been quite fun. All the upgrades are cheap enough to buy with collected free currency (I've maxxed out two characters already in a few days of playing), but it also rewards grinding by letting your characters level up through kills. I don't actually know what leveling does, it probably gives you a tad more damage and HP though.
Control isn't bad, but it can feel a bit "jiggly" sometimes. Still, it's responsive enough once you get used to it, and even tricky tunnel sections are pretty easy after a while. You can change the sensitivity if you want, I find medium to work well on my tiny phone. Since it's just touch-screen/auto-fire and a super button, it's easy enough to play. Sometimes your super glitches so it just charges your laser (R-type style), but this tends to fix itself by the next section.
When you get a good connection, MP is pretty fluid and quite rewarding. It uses the revival system, so it's rather satisfying to try and hold on through the hard bits until you can revive your dead team mates. Without a good connection it's like a slide show, damn near unplayable, although it seems to change level to level, and section to section. Don't know why. Very "spritey" sections slow it to a crawl sometimes, yet sometimes it's a smooth as butter on different runs. It probably doesn't help that my phone is pretty crappy, or that I'm in Australia (US/Japan/UK and Malaysian(?) servers I think. All vary a lot in connection speed, but there's no penalty in leaving a room and joining another if that one's connection is bad).
It's a PS/xbox port, to the point that there's still A/B control prompts, but it's a shoot'em up, so this isn't a problem. It's not exactly complicated. No actual exit button either, which seems to be an increasing trend in mobile games, so you've got to task kill it to close it properly. There's weird level glitches too (non-loads, flying backwards, zoom-ins, borked bosses), but just exit that game and jump back in.
The main starter character is pretty damn good, so you're not stuck having to buy something that can actually complete levels (at maxxed bought stats and lvl 6 it absolutely wrecks some bosses with missiles. This took me about two days to get up to, but I've been playing a fair bit). The other character I've got is a healer bear, which is insanely good and cheap to get. It looks crappy until you realize that the healing super is also a close-range bomb, and that when you get a few P pods shit starts firing everywhere. Stupidly useful weapon arrangement for a "support" character, that still does pretty good damage.
Anyway, try it out. Shoot'em ups are one of the few genres that mobiles can actually do well, and this one is quite good. Small footprint on your phone (<8mb on phone, 64mb on SD), so it can't hurt to have something sitting alongside Tyrian for when you're bored. Just for the MP aspect really.
Try and watch a few ads sometimes, just to keep the MP servers running