Hi judgmentday, great questions you have there. I have some great answers for you that'll hopefully save you tons of money mistakes that I made. I'll just ask that you bare with my answers below with some patience and an open mind.
First off, speakers are not driven by watts, they are driven by electric current. I learnt to understand this the expensive way, buying t a $2500 Parasound Halo Integrated and couldn't for the life of me understand why my 805S sounded so poorly. Keep an open mind here, cause this is where I'm going to help save you tons of money.
Now some quick important facts about the two B&W speakers you asked about. I would definitely take the 805D3 over the 702 S2 because I love the high detail resolution and the 'special' spec that the 805D3 is the only B&W with a 4.7ohm minimal impedance. This is very important because this makes the 805D3 compatible with most Class AB & D amps that cannot push low 2-4 ohm impedance. 702 S2 is awesome on its only at $4500 a pair vs the 804 D3 at $9000 a pair. If you're willing to give up resolution in exchange for the fuller sound of a full tower, 702 S2 is very good in its price range, awesome if you get it used around $3000 range. Note that 702 S2 has a carbon tweeter not diamond tweeter. Note that you must break in the 805D3 for at least 120hrs based on my experience and brace yourself for some really lean and bright sound the first 60 or so rollercoaster hours.
The 805D3 loves solid state and tube amps equally. First of all, I would recommend you hold off on Bryston amp unless you already have it. You want an amp that does 1.x 8ohm and 2.x 4ohm, the Bryston is only 1.6x at 300W 8ohm and 500W 4ohm. Without going into science details, the Bryston 4B3 is not generating electric current across a wide enough impedance to keep the B&W happy. Here's where I'm going to save you money. As alternative, try
For solid state, Marantz HD-AMP1. The meager spec will shock you what 35W 8ohm 70W 4ohm with Marantz current feedback feature can do. I have a 16x13x8 room and I cannot play at even half volume with this amp. You can get this from Amazon and return within 30days. Once you try this, you'll forever change perception of amplifier specs.
I tried 805D3 with a chinese Yaqin EL34 push pull amp and it worked well though I didn't really get the warm and fuzzy tube sound. Currently I'm using a 8W 300B SET amp with the 805 D3, works ok with female vocal, jazz...etc small music. In general, I use 300B SET when I want that holographic voice whispering in my ears feeling and the Marantz for large soundstage orchestral music.
Currently I confess I am still not driving the 805D3 with good enough gear, when I have the money, I would invest in a Mcintosh which I feel is closet to best of both tube and solid state worlds. If you can afford, you should try demoing the B&Ws with a Mcintosh MAC6300 or higher model with autoformer.