Tons of opinions and many of them really good ! Doing the GIK room stuff is a good start. A really good book, easy to read and understand is "Get Better Sound" by Jim Smith. Using this book and some rather inexpensive room treatments I was able to get my listening-room sound great.
For a room that size, horn-loaded speaker systems that are efficient may be the way to go as they don't require hefty power amplification for good output and man sound really good. Volti makes a speaker called the Razz that would probably serve you very well. It's very dynamic both macro and micro and could be very satisfying for the array of music that you listen to. There are a number of really good Class-A amplifiers that would work very well with those speakers. The Pass-Labs XA-25 is highly regarded and would provide plenty of power for them. And Pass-Labs makes the XP-12 or XP-22 preamps that are really great sounding as well. Those Pass-Labs products all have terrific reviews too. As for source equipment, if you must have vinyl, well then go for it. However, I have gone completely digital and don't even miss my vinyl anymore. Innuos makes a number of great music-servers and a BorderPatrol DAC will give your great digital reproduction with a very analog-like sound. All of the stuff I mentioned above would be well within your budget. In any event, enjoy your audio journey !