Just confused about where to start

Hello all,

I'm looking to add speakers to my audiophile setup which currently consists of (very high end) headphones. I want speakers for everything the headphones cannot do - simple enough. Problem is, I'm having difficulty deciding which gear I want to buy. I demoed a pair of B&W 705 S2's today and was very impressed. Unfortunately, my budget isn't that high. It's $1500 total, for the speakers and amp combined. Source is a computer. I listened to a cheaper pair of B&W bookshelf speakers (can't remember which, but were around $1200) and was not impressed. I am leaning toward bookshelf speakers but don't know if getting floorstanding at this price point would be a large increase in quality. The room they will be placed in is only 100 square feet. I am willing to buy used.

So, my questions, summed up are:

Is bookshelf a better option than floorstanding?

Is it worth looking at cheaper B&W models, or should I look at other companies altogether?

At least with headphones, I like a pretty neutral sound, if not a tad warm. Are there any companies that predominantly have this sound signature?

How should the room size inform my choice of speakers?

Congrats on the speakers I hope you love them! And good luck with finding an integrated that Sansui is Class AB since you were asking.  Never heard one but they do have a following. Looks like you have some good options and plenty of budget to find a good amp.
Project amp box DS2 seems like a good amp for the money. I think I heard one or a similar Project amp at a show and the system sounded great.
If budget is tight, nothing beats Yamaha with their AS 501/701/801 integrated amplifiers or their receivers like the RN803d that was mentioned earlier. I see no point in going second hand with budget gear: by the time you have had them refurbished, you may have spent more than on a new unit.
Howeer, you have not yet answered my question about your DAC/headphone amp: can you use it as a pre amplifier? If so, all you would need is something like a $200 Behringer A500 power amplifier.
I see no reason that the Lyr2 could not be used as a preamp for an amplifier. I suggest starting another thread requesting input for an amplifier to be used with your Snell speakers. 
@willemj Sorry, guess I didn't tag you in my blurb about the headphone amp.
This is the amp. It's stated that it can be used as a preamp with "powered desktop speakers"
So does this mean it would work fine with a power amp as well?

I'm creating a new thread as has been suggested and will tag you there as well.