There are several things to consider when generating passwords, but ultimately you should prioritize the length as opposed to complexity as beautifully illustrated here. The importance of picking something random, as you mention, to avoid social engineering naturally remains paramount, but if you can eliminate the need to worry about humans accessing your accounts, you only have to worry about computers. I would in that regard strongly advocate the use of masked mails for websites and services requiring a mail to sign up - i.e. by using https://www.abine.com/index or similar.

An unknown, randomly generated mail address with no relation to your persona is effectively an extra password. If you furthermore ensure to tunnel all masked mails to the same inbox closed in a two-step verified loop, you can quickly achieve very decent security. Of course, do take use of all provided security features on the individual websites as well.