(The MT is the Hebrew, so the KJV translators thought it was the obvious choice to translate from rather than the later LXX translation of the Hebrew. I would not just memorize from the KJV OT without checking first, as it may be quite different in Christological passages For Psalms, I would compare Brenton to the Coptic translation, and memorize from KJV or Brenton if not substantially different from the Coptic. I would check Brenton, NETS, and KJV for OT passages, and memorize from KJV if not substantially different, Brenton otherwise. I personally would memorize from KJV for NT.
You would have to check your Church books to see what translations are being used in them. But the literary quality is not great at this point. It is far more accurate than pretty much anything else available. Here is an Agpeya translated from the Coptic (even the Gospels): Brenton's translation is quite poor, but a much more accurate OT than KJV. Many Churches use Brenton's translation of the LXX for the OT prophecies, and many translate the Psalms from Coptic. We follow the LXX (of which the Coptic Bible is a translation, and in fact in many ways more accurate than the versions of the LXX available today). The KJV and its descendants uses the MT for the OT, which is not right in an Orthodox Church. You should be able to tell which of these your Church uses by how old fashioned it sounds. It is more understandable to youth who aren't familiar with the older English, but it does have some inferior translation choices, so it's a trade-off.
I think that eventually gained approval as well, but I'm not sure. Many still use that, but some have switched to the NKJV.
The translation originally approved to read in Coptic Churches is the KJV. Is there any particular English Bible translation used in the services of the Coptic Orthodox Church? I ask because I had planned on memorizing some passages of Scripture and I wanted it to be in conformity to the translations we used at Church. But, I am putting here to get a second opinion. I have already posted this on another forum where I got some good results.