In that price range I would say JL Audio 12W0 or 12W1 series. The Alpine Type S wouldn't be a bad choice. I see Image Dynamics in that range, but I'm not sure if it is the original woofer or a rebranded. If you extend your price range up a bit more to $200 or $225 you can get into some nicer woofers (Dayton, RE Audio, JL 12W3, Alpine Type R, Polk Audio, etc.). Extending your price range would also let you get into 2 10's for a bit more cone area if you are willing to give up a bit more room. With your music choice I would most likely port somewhere between 34Hz and 44 Hz depending on the woofer.
Amp choice? How much power? Two more questions that affect woofer choice. If you have to drive a low ohm load to make power, you will need a dual voice coil woofer.