Is apkmirror.com safe? Is it safe to download and install Google Play from apkmirror.com? How can I check this is a safe download?

Backstory:

I had to factory reset my original Samsung Galaxy Tab as it refused to start up. After the reset, I haven't been able to update Google Play. Every time I try, it crashes with '(process com.android.vending) has stopped working'.

I've seen multiple references to the site, but nothing official from Google.
Apkmirror.com is run by the same people behind AndroidPolice.com, one of the biggest Android news websites. All uploads are manually vetted and approved, and only free apps are allowed so you won't find any 'cracked' apks or 'warez'.

As you already have the Play Store installed, only an apk signed with the same key as the currently installed version will be able to upgrade the app so this is an extra verification of the apk you download. Therefore, if you download the app from Apkmirror.com you should be safe.

Personally, this one of the only sites I would trust to download apks from.