Building a New Listening Room on a Budget

My wife and I have been considering our next home, and recently signed a PA agreement with our builder.
The basic layout of the house is set but not finalized, which should be done within the next week.
I will have a dedicated room for my audio needs.  It measures approximately 25' x 14', and is not a perfect rectangle.  Doing my best to describe it, there is a 14' x 14' square section on one end and a 11' x 9' section on the other.
I plan to set up in the larger section, and use the smaller section for record/music storage.
The utilities room for the house is in the adjacent room, and I plan to have the internet router in that room and run a LAN cable from there into my listening room for streaming purposes.  I already plan to have at least one dedicated power line installed.  Should I add a second?  And, should I do 20 amp or 15 amp?
I'm planning to insulate the ceiling and walls adjacent to other rooms inside the house to avoid disturbing my family with the noise.  The floors will have carpet and walls will be traditional drywall.  
Beyond these things, what should I focus on that will not cost a ton?  I have read Robert Harley's article on his dream audio room build, but he spent way more that I'm willing to.  If I had to put a limit on it I would say around $10K.  
What other areas should I focus on?  
Thanks in advance!
10K, or WAY less, I’d say. 1 20 amp dedicated and an outlet every 4 feet @ least two different circuits on the SAME rail at the mains.. Three total 1 20 dedicated..

I’m not much of a studio look kind of guy.. I use HEAVY retractable curtains and I’m working on Spring bass traps.. Mainly to cut down on the studio look of clutter. I would stay away from foams most of them are OK at best acoustically. Square traps are the better of that type of bass trap..

Sure nice when a plan comes together. 35 year on mine, I’m just now able to finish the work after adding 4 rooms AFTER work.. Very little help.. Just me my hammer my saw...NO NAIL GUNS either. Double dip galvanized nails too.

Sheet rock was 5/8 fire rock on the lids and 1/2 on the 2 x 6" wall studs.. I had help on the lids a kid help me.. Everything else I bucked up.. I was a BIG guy back then. I worked in the nude too.. Just a nail pouch and work boots..:-)

I glued and nailed the T&G 3/4 ply too, NO NOISE in that room..

The second room has a built in 128CF bass traps on one end of the room.. I’m droolin’ to finish that one.. open the traps and WALA perfect room almost.. lol It’s also my indoor work shop too..
GEAR everywhere. :-)

On that kind of budget I would do only the few things that make a huge improvement for almost no additional cost: 

IF you sheetrock anything, 5/8" blocks sound about 15dB better than 1/2" but costs almost nothing more.  
Use a solid core exterior type door. You can buy architecturally designed interior doors made for sound abatement, but they can cost a small fortune and be hardly any better than an ordinary solid core or exterior door. The exterior part matters because you want weather stripping. This one thing right here costs very little but makes a huge difference. 

ONE SINGLE 20A line.

That's it. The only construction I would do is if your layout makes it cheap and effective to add an interior wall for sound control. The space between could then become a bass trap. But you have to find someone who understands acoustics and balance that with your floor plan and use.  

Honestly from everything I have seen going from planning to construction and then ongoing system improvement, I know everyone loves to go on and on about the room but my experience is you get a lot more bang for your buck from things like Synergistic HFT, Townshend Podiums, Cable Elevators, and wire, than anything you can do to a room for the same amount of money. 

So not saying don't spend money on the room. Those few things I mentioned are huge. Mega. But anything beyond that, if it means not having money to do these other tweaks, then you have shot yourself in the foot, committed own goal, and put the cart before the horse.
Thanks to all for your responses.  Very helpful!
Ruminating on a few things:
- Stupid question:  Can 15A components be plugged into 20A outlets without a power manager?  I have a Niagara 7000 and know that it is fine with 20A or 15A, just not sure about plugging in directly to these outlets.
- The room is in the basement, partially underground.  Two walls are outside walls, brick covered with studs and drywall.  One of these walls will have an egress window, the other will have only dirt behind it.  The other two walls will be barriers between inside rooms of the house, one of them being our family room, and the other being the utilities room.  I'm thinking to insulate both of these walls with rolled insulation.  I could spray foam them at higher cost but wondering if it would have any benefits?  Ceiling will also have rolled insulation unless I hear of a better way.  BTW, above this room is the walk-in closet of our master BR.  I do not want my wife to complain about the noise at night.  At least it's not directly below the sleeping area but we all know how annoying it can be to deal with noisy neighbors in apartment settings.  That low rumble that persists.  Don't want that.
- 5/8" rock is a great suggestion.  I already requested this with the builder.  Sheetrock guys will probably curse me.  
- In my current room I have the equipment rack to the side of the speakers rather than between them.  I have heard this produces better sound but not sure I can attest to this.  I do have the option of running it this way in the new room as my speaker cables are 16 feet long.  Not sure if this is important to consider but thought I would elaborate.

Thank you!

A lot of good tips mentioned here I wished I knew before I got started on my room on a budget. I particularly like the idea of using thicker insulation, carpeted flooring, the 5/8" sheetrock is a great suggestion, run plenty of cables, use a more insulated heavy duty door with foam seal all around to keep more sound in. For the walls, if you can meet the ceiling at a 45 degree angle it would eliminate a lot of in room corners that is usually responsible for excessive bass.
Wall treatment is a must in a dedicated room! more parallel walls to deal with than in conventional living rooms. Stay away from acoustic foam or use very sparingly, a dead sounding room is the last thing you want.   
Below are some links you might find interesting wrt your proposed room.  
The electricity delivery articles offer similar recommendations with a few specific recommendations that vary somewhat between articles. 
To the question of one vs. two or more dedicated lines, most of the linked recommendations address multiple dedicated lines.  Michael Fremer from Stereophile recommends only one line to power the whole system to reduce the risk of ground loops but the linked articles do not necessarily support that recommendation.  IME, you shouldn't have ground loop issues if all the dedicated lines are of similar length and all terminate on the same side of the electrical panel.  My 3 dedicated, 20A lines are dead quiet.  You need to make that choice carefully as it would be hard to add new lines later.  You have one chance to easily construct and finish your room during the initial construction so I suggest looking at the articles, and considering the following when deciding how to wire the room;
  • your system's physical layout and potential future changes (i.e., front end components on a side wall away from the amplifiers, monoblocks near the speakers, etc.), 
  • power needs of your gear and particularly large power amplifiers (look at the  DTCD — Dynamic Transient Current Delivery thoughts in the Galen Carol article), and 
  • whether you might want certain types of gear on a different circuit (i.e., in the event you want to use a conditioner on some gear but not all)
Definitely have the electrician run a different circuit (separate from the audio gear) for general use outlets for things like lights, televisions, where you plug in your computer, etc. Also, consider a whole house surge protector.  If the audio lines will be significantly different lengths, you may think about setting up a subpanel and then running only the audio lines from that but you can have that discussion with the electrician.  Links below: