This app was mentioned in 4 comments, with an average of 0.75 upvotes
I use FlashScores and this seems to have everything you ask for. Really simple and can favourite games and teams to notify you when an important decision, goal, win, red card etc. happens. I use it mainly for football here in the UK but it covers a wide range of sports and a lot of the stateside sports too.
I'm not entirely sure what the difference is between FlashScore and FlashScores (with the plural) both made by the same dev. and both free. If anyone knows I'd be interested.
FlashScore android app: https://play.google.com/store/apps/details?id=eu.livesport.FlashScores_co_uk Website: https://www.flashscore.com/