I am now at the BR of 6.7, and I got the Imperatritsa Mariya. Since it has very bad anti-air and is probably slower, how do I avoid air, and how do I even stock grind this thing? Do I just research the APHE first?
Virtually nobody is using planes at that BR; AA capabilities or the lack thereof are only of the most minor importance.
Do what everyone else seems to do in 6.x BBs- focus on cruisers and DDs, then go for bot BBs of your BR or lower. Avoid 7.x BBs, especially if player controlled.
Try getting damage and fire control done first; your HE has got a lot of filler, and Mariya has got the best RoF of all 6.x BBs, so you should be doing fine during this initial grind if you ignore BBs.