IIRC Rayman Jungle Run and Rayman Fiesta Run are not at all annoying about in-app purchases. I paid once for the game and that's it, I don't even remember what was available to buy, cosmetic stuff probably. They're great fun and I highly recommend them.
The latest iteration, Rayman Adventures, is free-to-play and so suffers from the usual mobile free-to-play tropes. It also suffered performance issues on my (good) phone.
Rayman Fiesta Run (Google Play Store) got obnoxiously annoying to the point they included forced video ads of Rayman Adventures.
Rayman Fiesta Run (Amazon App Store) has some UI issues (like buttons reacting at press rather than at release potentially purchasing pay2win stuff unintendedly), but at least it doesn't have the forced ads.
When I purchased the game at launch date, it didn't have the pay2win stuff, and it was really enjoyable, but eventually the updates degraded the game experience.
If I ever purchase a mobile game again I'll certainly backup and cherry pick the update which gets the best balance between less bugs and less mis-improvements.
The latest iteration, Rayman Adventures, is free-to-play and so suffers from the usual mobile free-to-play tropes. It also suffered performance issues on my (good) phone.