:)
This SG should be a fine guitar for you to advance on, I recently got a low end gibson [The Paul] and it's got a fine neck,most SGs i've seen do as well. Gibson pickups are excellent for a wide range of sounds. I love my Gibson, despite a couple of minor faults [mainly the pickup selector switch] and think you would find this an excellent guitar which will,hopefully, keep you happy for years.
Up to 1k, I'd look at Yamaha S(B)Gs or AES models,Esp [EC]300/301s,Most Gibson Electrics,Gordon Smiths (if you can find them), Tokais,Dillions and Raven.
Laney and Marshall [I'm biased,I'm British too] make some damn fine amps in the 30 to 50 watt range, and i like the sound of most of those...but i know little about amps as such.
Hopefully you can get an excellent guitar from any of those makers and a nice amp for under $1000.
Good Luck.
Accuracy,you say? hmm interesting concept..