Unfortunately I've also had some problems with Playstore lately on my Classic. The first was not being able to sign in at all, and discovered that the culprit in this case was a Play Services update from Aptoide. Once I uninstalled that update things were OK. That was a couple of months ago.
Over the last couple of weeks when I try to sign in to Playstore, the screen goes black! I have to hit the back button, clear the Playstore cache, then it's good to go again. That's happened to me twice. What's causing this, don't know, but I'm just putting it out there for info.
Just a note, I do use Playstore for some apps, but I always delete the account when I'm finished. However that only deletes the account on the box; you also need to login to your Google account to actually sign out of the account on the box. Now, all auto-updates are always turned off. Inconvenient, but it's a work around for now.