I grew up influenced by not metal bands that shred (although I love metal), but punk bands that have shreddy guitar, like RKL and Bad Brains. So, my practicing back in those days worked on facilitating speed and accuracy with alternate picking and fast, staccato palm muting. The tapping stuff and sweep picking I picked up later, although I find myself using those techniques pretty sparingly and more in a riff/melodic sense, as opposed to an overt shredding sense.
So, I guess because my lead playing is very alternate picking based, I tend to like amps and guitars with a very immediate, percussive attack. My amp of choice for a long time was a VHT/Fryette Pittbull Ultra-lead; everything is tight and percussive through that thing. For guitars, my McCarty, NF3, JA-15 and 305 all have a great punchy attack, although for more shreddy stuff, I typically grab the first two.