Copper pots have amazing heat conduction. There is almost no way to have a hot spot unless you set the pot over a welding torch - even then, if you move the pot around a bit, it will even out.
Because it is so reactive, copper pots are almost always lined with something less reactive.
It is an absolute dirty bitch to polish back up after you use it. If you DON'T polish it, you slowly lose that magical heat conduction due to the outside oxide layer that builds up. Still evens out the hot spots, just takes longer to get hot.
Almost ideal (from a convenience sake) would be a stainless pot with a heavy copper base that was fully enclosed in stainless. No polishing, no hotspots.. downside is it will hold the heat well; too hard to do fast temperature changes. Also, if you overheated it it would crack the base off (bimetallic expansion).
They're expensive as hell, but I see no point in getting one larger than 1 quart - and then, only in a saucier shape, to use for butter sauces.
For anything larger, all-clad and probably others make copper core stuff that is WAY more affordable, and almost as good. It will heat up a bit slower, however.