unwanted apps keep installing their own after reset

[AC Question]

Before, my phone works well, but as time goes by there are terrible moments happening on my phone. Ads keep popping up every time I am connected to the internet or when I turned on data. There are apps keep installing even if I didn't press anything. Because of this, my phone is lagging. I went settings, uncheck the unknown resources, and uncheck the automatic restore. Unfortunately, things went wrong. Nothing changes, my phone is still lagging, and there were apps being installed on their own. So I made a decision. Reset my phone. But even in the factory reset, I'm having a difficult time. I pressed many times the "erase everything" but nothing happens. An hour passed by my phone was finally reset! Phew. When my phone turned on after the reset I turned off my data connection and even the wifi. Happily, my phone is back to normal. Nothing ads pop up, nothing apps were being installed and nothing went wrong. But just to make sure that bad things will not happen again, I uncheck the unknown resources and uncheck the automatic restore. I am about to sign in to my gmail account so that I can use the playstore, but things went wrong when I have connected to the internet again. I have not yet signed in to my google account, nor open the playstore (because I haven't set my account yet). And guess what? There were ads keep popping up, there were apps being installed. (very annoying because even if I uninstall them they keep coming back) my phone is lagging. I can't even type properly in the message because my phone suddenly backs to home and keeps saying "android system has stopped". There are also another things that pop up. Like "system.bin" "sys.update" and another one like ("andoird.sms.push" I forgot). I also check the running apps. And I stop them, but they still keep coming back and run again. I don't know what to do because every time I am connected to the internet this is what happens! What should I have to do?