Start taking a COLD shower after EVERY class. This is most helpful with those day after aches & pains, not to mention helping ward off staph & ringworm. Contrast showers are also a good option if you don't want to go 100% cold.
BJJ practice + Contrast Shower = Sleeping like a baby.
As far as the neck goes: ice massage, gentle rom stretches, massage, maybe some heat after the first day. Comes with the territory. If I remember correctly my neck took a good month to get used to bjj.
Sounds like you've got a nice school. I'm chomping at the bit to get back into it.