I generally prefer to have a shotgun for outdoor or big, high-ceilinged spaces. The Sennheiser 416 is a classic for a reason. Some people don't like them these days, but I still do. I actually opted for the Rode NTG3 over the 416 personally, because it sounds very, very similar, but the Rode has a slightly larger "sweet spot" that I personally find a bit more forgiving. (The counter argument to that would be that it's not
quite as tight or focused as the 416, but I haven't found that to be a problem personally.) Both the 416 and the NTG3 are RF condensers, so they keep working even in very humid conditions. And the Rode is a little lighter physically.
For indoors in more normal rooms, I like a tighter cardioid generally over a shotgun. Something like the Sennheiser MKH50. If the room is really quiet and you're trying to pick up two people sitting next to one another on a couch, you can even go with a wide cardioid.
Agreed that omni lavs are a good idea to put on talent.
Zaxcom body packs are great but out of my price range, so I use a Rode Wireless Go II, though the new Wireless Pro is an even better option. Even if there are dropouts on the 2.4GHz broadcast to camera, everything gets recorded to the internal transmitters, so you're covered there. The new Wireless Pro actually records in 32-bit float, so you don't have to worry about clipping at the record stage.
I also wouldn't personally want to use a Zoom H6 -- I have before, but it's a pretty big compromise IMO. The pres aren't very good, it's kind of noisy, but maybe even more importantly, it doesn't have many great power options (IMO). If you like Zoom, the F6 is far, far superior, and can be run off of NPF batteries. I have an F6 as a backup to my Sound Devices MixPre 6 II. I like both of those units a lot, actually, and they both can record 32-bit float, as well.
I would also ask the director what they want to do about timecode. Are they planning to rely on audio sync in post? Or do they want dedicated timecode? If dedicated timecode, that's a whole 'nother set of things to think about.
You mentioned the problem in the past with extraneous noise on the external mic pickup. That's definitely always a concern, and you're right to think first of what mics might best help mitigate that. But you'll also probably end up spending time cleaning up some things in post regardless. I use a little bit of everything: iZotope RX, Acon Digital, CrumplePop, Hush Audio (one of the very best, IMO), and even the voice isolation plugins in the NLE. I'm primarily a Final Cut user these days, and the latest included voice isolation is actually very good IMO - oftentimes it's all I need. Oh, and quite a few people like the Waves Clarity Vx plugin.
Regardless of all the above, exciting news that you're working on this project! I have really grown to love production audio for picture over the past few years -- it's exciting (usually non-boring) work, and it's fun to be a part of a creative team all working to make the best production possible within all the insane limits faced in a video-centric environment. Congrats!