I can't say that I'm fairly competent (I'm not able to use a lot of different equipment items), but my choice is
ESP LTD EX-307:
LTD, because it is inexpensive
EX series because I like explorers))
307, because I think that 7-strings provides more features for metal
Amps... I like mid-scooped powerful death-metal tone. Well, I've got it with both amps that I tried to use: Peavey 6505+ and it was easy, 5 minutes settings; and Randall rg50tc, but with Randall I had to use additional EQ in loop, and setting takes a long time.
I like to use a Bogner or Marshall amp with an overdrive pedals or a nice warm tubescreamer and I like to use the same mic and cab as the rhythm tone. Though the sound mostly comes from how you play I have noticed that if you use a different amp for lead tones when recording that the contrast helps make the lead sound stand out and can appear more fluid/warm.