The two groups I play EH with like to get random investigators instead of picking, which is fine, though I do think it can ramp of the difficulty a bit. And the designers seems to agree, since the rulebook tells you to choose an investigator
When i am playing by myself, I like to choose since you need to have a diverse team and with some AOs you "need" to have certain investigators.
So far I have this list:
Shub - Leo Anderson and Diana Stanley as my gatecloser/spellcaster since she is also good in combat.
Cthulhu - Silas
Yog-Sothoth - Akachi and more spellcasters than fighters
Yig - Leo again as well as an more fighters than usual.
Most of the time I play with 4 investigators and have 2 fighters, 1 spellcaster and 1 support character, sometimes I use Charlie Kane but usually it is another spellcaster with fleshward, bless and such.
What other Investigators have you found works well with particular AOs and how do you and your group prefer to pick investigators? I haven't got MoM yet, but I would like to hear about the new investigators and AO and what combos work both with the expansion and the base game.