So for someone who really hasn't read much of Fantastic Four, other than the early, early "Heroes Reborn" issues, how easy is Hickman's run to get into?
I've heard it's great, but honestly, I'm mainly interested in it, since it seems to have picked up where DnA left off with the cosmic heroes. I know that he's used Annihilus and the Negative Zone and I've heard Black Bolt is back, there's a Kree/Inhumans war, and Ronan is involved in the War of Four Cities. As a fan of DnA's work, will I like Hickman's?
Well, in theory, #604 should be a good jumping on point as it should be the begining of a new story arc.
I haven't read any Marvel cosmic, so I can't really compare Hickman's work to DnA's, but as for Hickman picking up where DnA left off, given that all of those things you mentioned-- Annihilus, the Negative Zone, Black Bolt and the Inhumans and Ronin and the Kree-- all originated in the Lee/Kirby FF run, I'd say it's more a matter of Hickman bringing all of those elements home than anything else.
ETA: That said, appropriate respect is paid to DnA's work as all of those characters and elements seem to be picked up from where DnA left them.