You're heading right down the path I travelled recently. My goal was to keep cost down (important when you build). Thanks to my builder

I didn't quite get everything I wanted in the room. If you're going to finish the basement anyway, the space is "free" and the additional expense minimumal (in my case about $200). The primary advantage is privacy (man-cave stuff). The goals for the listening room is two-fold, for the room to "sound" good and to be acoustically isolated from the rest of the house.
1st step is to size the room (so that it will "sound" good).
Keep room proportions in ratios like 1 x 1.62 x 2.62 to minimize standing waves. This is the ratio I followed to arrive at an 8 ft x 13 ft x 21 ft room. This is the classic greek architectural proportions but a couple of smaller ones exist too. Bigger is always better as it will help minimize room reflections. Ceiling height will probably be your limiting factor. Account for reduced height for a drop ceiling.
2nd step is to pick room materials/construction (so that it is isolated).
Use an acoustical drop ceiling. This is the "mistake" I made with the builder. I specified gauge metal "Z" channels to suspend the drywall ceiling. He refused and screwed the drywall directly to the ceiling. Now I hear the washing machine, dryer, footfalls, etc. on the floor above even though the ceiling had fiberglass batts added. So my advice is to simply install the drop ceiling. This will be about half the extra cost to make it a "listening" room. (Hint, don't use recessed light fixtures on the ceiling as I find that they sound to transmit too.) And try adding insulation on across the top of the acousticall pads.
Build the interior walls using staggered stud construction. In the U.S. we'd start with 2x6 top and bottom plates, then 2x4 vertical studs. One set of studs aligns along each edge of the plates and they're staggered so that the studs from one side doesn't touch those on the other. Then add fiberglass batts. This makes for a very effective sound isolation barrier. This shouldn't cost more than $100 extra.
Use a weather sealed insulated fiberglass door. They come with a wood grain and can be stained or painted to be quite presentable. Depending on the quality of the doors in the rest of the house this could be a cost savings.
Use flexible insulated ductwork to serve the room. It's cheap and easy to use, but reduces air flow substantially (so don't let the builder use it elsewhere).
Wire separate circuits to serve just the listening room and locate them at the top of the circuit breaker box. In the U.S. houses are wired in either 14 gauge for 15 amp circuits or 12 gauge for 20 amp circuits. Go with the heaviest possible. I went ahead and used cryogenically treated 20 amp hospital grade receptacles (three cost $100).
Room finishes are up to you, just figure on proper room treatments afterwards (season to taste).
The effect is (except for the ceiling transmitted sounds) an eerily isolated feeling that took some time to get used to. In fact there are times I still leave the door open. Weird to walk out of the room and realize that the furnace which is only 10 ft away, is running. The room is warm (all the insulation and the basement itself is already well insulated). The privacy, the ability to listen at lower levels due to reduced background noise, and the ability to listen when I want are all wonderful.