what to buy first

The MA Platinums are incredible speakers; very neutral in my opinion.  
As I believe the Benchmark can function as a preamp--at least for digital-- getting a power amp rather than an integrated will give you more options in the future. 

You'll want a tube amp with a lot of power.  Audio Research is a personal favorite.  The Primaluna Dialogue Premium HP is reputedly excellent for the money and easy to tube roll to taste (I've only heard their entry level model).  I'm sure others can give you many more options.

I agree with swamp & George  - The Benchmark DAC/Mac-mini is at least very good (DAC1) to xlnt (DAC2, and 3) - you did not say which one you have.

Get speakers you like (say Vandies or Maggies) and then buy a tube pre-amp (say a used Audio research).  The Benchmark amp is outstanding by all accounts and the tube pre- will give you the warmth and liquidity you want.  After that you can try some things to reduce noise, but the Benchmark DAC is so well-designed that the usual tweeks for inferior DACs may no help much.

So focus on room treatments after getting your speakers.

A lower cost option is a stack of Schiit units

+1 for speakers first. IMO every manufacturer has a 'house' sound and variations within that. Even if your amp or source is "isn't good enough" for optimal sound the speakers can deliver you now have an idea where to go next. Personally I don't look at specs because I've never seen a spec that will tell you how it sounds. For that reason YOU need to decide what speakers you want. For a suggestion I would recommend you listen to Dynaudio - Magico - Raidho - YG. They all sound different. Again YOU need to make that choice.

For tubes I had Octave in the past and they make wonderful sounding amps that are pretty bullet proof.

Best of luck

Thank you so much for the above responses.  It is difficult for me to listen equipment in my area.  Are there any good audio shows coming up that I might attend.  I know about RMAF in October, any sooner?

That's a huge room, are you really set on tubes?  I'd get a big pair of maggies and a 400+ watt solid state muscle amp and a pair of subs.  Then invite a bunch of friends over for the concert.  I hope your neighbors don't live too close. Oh yeah get a tube pre if you need something to glow.