what to buy first

While different makes and models of speakers clearly sound quite different and some measure out better than others in instrumented tests, they can only work off the signal fed to them. 

The SR 7011 is a decent AVR, so it's likely that better speakers may give you sound quality that you like and enjoy better, i.e., more and deeper bass extension and possibly better tweeters.  But i also agree with swampwalker above that amplifier quality can be just as important.  And in my experience cables can also make a big difference, although many swear that is "fairy dust". 

I am currently running a Denon AVR-X5200, which is pretty high in the Denon lineup, but using a separate class A power amp, which is a Krell FPB-400cx.  I do believe the Krell improves the quality of the sound over the built in amp in the receiver.  If you know what amp you want to end up with, I guess you could use it with your receiver and see how it compares.

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?