The best possible viewing surface is a fixed frame screen with a nice velvet border around it. The wide framed screens, like the Carada Criterion, are by far the way to go if the room allows for it.
Now, I run a motorized screen with a flat panel behind it and I definitely use both of them, but the flat panel generally gets more of a work out for day-to-day viewing. Still, I wouldn't trade my projector away either.
Now, you've justified the lamp cost, but you have been sold a lie. There is no lamp, outside of LED models, which truly can claim 4,000 hours. Generally speaking, lamps should last at least 1,000 hours, but you should budget for a replacement lamp at 1,000 hours, then be thankful if you get more quality viewing time than that. If you do, then that's great, but if not, then you won't feel ripped off when you have to install a new lamp.
Yes, a STRONG air current can make a hanging screen sway. But, the bar at the bottom of a quality tab-tensioned screen weighs 30 or more pounds. So, it takes more than normal air movement to get that thing moving. I've never tried to see how much air it takes, but my HVAC system has never bothered it, nor has my moving around the room, but it depends on how much air you are talking about and how close it is. They do sell 'vent covers' for HVAC systems which you may want to consider if necessary.
Still, if the room is always light controlled, then you may just be happy with a fixed frame screen. It is a choice and decision entirely up to you, which doesn't help you figure things out really, but it's safe to say that both options will give you high quality results.