Many FMs have given good solutions which would help you achieve your goal quickly. I am suggesting a difficult route but something that would get you great bank for buck:
Speakers:
I have toggled between two-way speakers (Elac BS-243), Co-axials (Tannoy Sensys) & Full-range horns (Fostex DIY by FM
@manniraj ). Of the three, FR horns sound the best for Indian classical music (not sure but I feel that they are soulful), followed by Co-axials and then two-way speakers. I felt the same when I auditioned Frugal horns by FMs Vivek Rao & Manniraj. I am no expert with the science of speakers but would suggest if you can have Frugal Horns DIYed in Pune(There is one on sale in Bangalore but you might lose money in shipping it). The mids from Frugal Horns are at different level. The immediacy of the speakers make them a great gear for vocals. These speakers are keepers for long time. You can connect with FMs mentioned here about the simplicity/complexity of the build and see if this is an explorable option).
Budget :
13K - 15K.
Amplifier:
Marantz PM5005 is really good. You can also go SMSL Q5 Pro which is a great solution due to its VFM DAC. Even simple Onida/Philip DVD player becomes a great source when you use their Coaxial or Optical out. SMSL Q5 Pro also lets you connect computer audio as well through USB. They sound good for medium sized rooms (10X12 or 11 X14).
Budget
: 10K-20K