I've got 600w into a single 4ohm DVC 12" sub, wired down to 2 ohms. JL Audio Class D amp, and Rockford Fosgate sub. Never a diming light, never a problem. If you get a quality brand 1000 watts and nothing else hooked up, you shouldn't have any power issues. I still have full control of the stereo with the stock controls. However I added a gain nob for the sub so I could turn it up and down from the front seat. I like that they now use RJ11 (phone jack) cord to connect those...if a cord get's damaged you don't have to get a new nob..
Different strokes for different folks. Lol I've got a Massive Audio 10" dual 4 ohm voice coil sub in a 1 cu. ft. sealed box. I'm using a Kicker 800 watt (rms) to push it. I've got the sub wired so it's a 2 ohm load on the amp which is actually about 600 watts. Could be a little more as the amp birthsheeted at 888 watts rms. No dimming lights for me either. I still need use of my trunk, that's why I went with a 10" in a smallish box. I would recommend going with a quality LOC (NVX has a good one) so that you won't deal with bad 6 rolloff as you crank the volume up. I am currently running mine off the Scosche LOC and it's noticable. I'll post an update after I install the NVX LOC.