For me, New Avengers is the only must read this week. I've enjoyed the interaction between the eclectic cast of characters. There's much intrigue and suspense in trying to save the world and not kill each other in the process! I do wish Marvel wouldn't be so ridiculously caught up in name brand recognition and just call the book Illuminati. Or at least Avengers: Illuminati. But, that's a pipe dream on my part.
I'll likely pick up Hickman's other Avengers title, but I am growing weary of that one. Things need to change or its getting dropped. Also may pick up Hulk and Spider-Man this week but will thumb through it first to be sure.
I agree - "New Avengers" is a very clumsy title to put on an Illuminati book. If they have to have Avengers in the title, call it Avengers: Illuminati, as you suggested.