Don't forget the "recording-chain"
nr 1: the drummer itself
nr 2: the drumset and its tuning
nr 3: the mics
nr 4: the preamps
nr 5: the converters
nr 6: the cables
I guess, with the mics you selected you can't go wrong.
SM57 is cool, e604 on toms should be working. Had them when I started recording but find them way too bassy.. but that could have been a problem of positioning in my case as well.
I like the audix d6 more than the d112 but you should try it, or even order both and compare them and then send one back.
Something I would consider to do:
Start with 2 mics or 4..
Buy very good overheads as they capture your whole kit. You can even get an amazing drumset sound with 2 overheads.
Then you can add other high-quality mics as well.
Also consider to buy a good preamp/interface.
When I started recording I thought:
"Well, I'll buy this alesis firewire mixer, shouldn't be a problem" - it was -> the alesis sounds like sh*t ... you won't recognize it but later you will hear that they just sound bad..
Good luck with recording