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4" lift with 35s and 6" lift with 37s is what is common. But you can run 35s with the 6" lift and still look ok. I'll second the vote for 35s simply for the fact that stepping up to 37s really puts you in the range of needing to regear (another $2K), for 2 reasons. 1 power loss with the 37s will be significant 2 the strain on an auto transmission is pushing the limits especially if you ever tow anything.
I never recommend going over 4" with any SD. Carli and BDS make good suspension systems for that truck. Need more ride? Put a King 3.0 triple bypass shock on each corner (firmly valved, use the adjustable bypasses to tune).
Even with just 4", you're inviting all kinds of alignment gremlins. Nothing that isn't easy to fix, but your best bet is to do most of the alignment yourself as you have unlimited time in the driveway for attention to detail, techs have limited time to diagnose and fix things so many people get nightmare results. On my '17, the drive shaft gets dangerously close to the exhaust.
You can use Bushwacker cut out fender flares for 38" tires on wide wheels if you're going the hardcore route. But I recommend just 35-36" tires usually. I'm only doing a 2" leveling kit adn 34.5" tires on my '17 F250.