I want to search for games, or any must haves for android phones.
Although Google play is a nice answer, Google play has such wide variety of apps, and lists. It doesnt necessary mean if it is on google play, it is already useful. Imma tell you some useful apps Ive encountered in my life, and I still use them until now.
Facebook and messenger app - if you like social media, and doesnt go to computer A LOT. both app is very helpful. Use messenger for quick connect to your friends. and FB app to be updated. :)
exp game - you said you love to search for games, exp game does the same, although games there are already filtered. It will redirect you to goole playstore when oyu download a game, but the good thing is, its already reviewed so expect to see lots of good games there. theyre also open for app beta testing if you want to be one.
Notepad - one of the useful apps Ive ever used. For quick notes when you need it specially since I work already, I dont have to bring pen and paper always.