First, how much do you weigh? Sprung Brooks saddles (like the Flyer) have stiff springs that don't really compress unless you're more than 175 pounds. The springs add another half a pound to the saddle, so I wouldn't recommend them unless you're heavy enough to get the benefits.
I'm
#220 and I use a B17 Flyer Special on my Riv Road Standard and a B17 Flyer on my fat bike. I appreciate the extra shock absorption, but the springs don't make the leather any softer.
Brooks saddles don't stretch very much; your butt breaks into the saddle probably as much as the saddle breaks in to you. Other saddles similar to Brooks: Velo Orange, Rivet, Gilles Berthoud.
I haven't tried Selle Anatomica saddles; the reviews say that they're quite comfy because they stretch, but they wear out quickly because they stretch.
I find that the need for padded shorts depends on the type of intended riding.
I can ride any of my bikes (the other two have non-sprung B17s) for a casual ride (10 miles or less, slower pace) without padded shorts.
I prefer to wear padded shorts whenever I'm riding aggressively or longer distances. I can ride >100 mile days on my Brooks saddles.