For your requirements I can wholeheartedly recommend the RS1... well, except for classical music. With any other genre, it's one of the most engaging and fun headphones out there. For $1000, you should be able to get a used one and a nice tube amp. You can still get the LCD-2 or another phone later as an addition.
If you should decide to get an RS1 I'd recommend to look into a "vintage" one as they sound slightly softer and warmer than the newer RS1i. There's absolutely no harsh treble on my (rather old) RS1.
See, the RS1 is nice, but I don't think it really compares to the GS-1000 or the T1.