First off, since you are setting up an open room in a basement with a concrete floor, you'll want a lot more sub than the little Klipsch. You'll want a pair of 15's as a minimum in an open basement, and 18's or 21's would be better. I'd look at Hsu, SVS, Rythmic, Monolith, or PSA for sub brands, or if you can do DIY subs, look at the VBSS design, or the Devastator.
Those are fairly long speaker runs, but you will be fine with Monoprice copper 12g speaker wire at those distances.
For an AVR, I'd recommend the Denon 3600H for 7.1.4 if you don't mind adding an extra amp for the Atmos channels (Dayton Audio and Audiosource sell suitable amps for ~$125. If you want everything in one box, you'll need an 11 channel receiver like the Denon 6500H. If you want to stick with Pioneer - I think the 904 is their 11 channel model.
I doubt you'd see much (if any) benefit to adding an amp for the B&W's unless you drive them to insane levels. They aren't that efficient at 88db, but I think any middle market receiver should be able to drive them just fine.
Is this basement currently unfinished? If so, I'll add my standard suggestion to go ahead and pre-wire for a 9.x.6 Atmos system as it's easy to do before drywall and hard to fish wires through later. I'd also run a conduit to your projector or TV from your equipment rack as one day the HDMI spec may change or HDMI may be replaced entirely. Speaking of HDMI, you'll need a fiber optic HDMI cable for any run over 25ft (and a certified one up to that point) for 4K playback. If your running it in wall (even in a conduit), I'd check it before install to make sure it passes a 4K/60 signal. I'd run Ethernet to my A/V rack for any streaming you want to do. Now's the time to do any soundproofing too, though it may be a moot point with an open basement. Save some money for acoustical treatments as they make a difference in what you hear more than any component or speaker.
7.4.4 Theater Room: JVC-RS500, Silver Ticket AT 2.35:1 142”, Onkyo RZ830, Anthem PVA-7, Panasonic UB420, Apple TV 4K, JBL Studio 530’s, Dual Driver VBSS
3.1 Living Room: Samsung 64” F8500 Plasma, Anthem MRX 300, Dynaudio Audience 52’s, Dynaudio Audience 122C, NHT SubOne, Roku Express (2019)