For affordable cans I like the Sony MDR-7506, with the pads swapped for the Beyerdynamic EDT250V ones. They aren't the most detailed (as you'd expect for the money) but the response curve on them is really nice and flat.
Re: drum machines, the Roland TR-6S is a great little box that does a lot.
Hmmm - cheers. That might be one for further down the line.
Cheap(ish) headphones recommendation? All mine are Bluetooth.