Unfortunately you will probably have to do some experimentation to find out the exact right amount of rest for you before and after a long distance. For a training run of 10M or over for me, I try rest the day before and the day after, sometimes 2 days after depending on how I feel.
For a race, I do a more traditional taper -- I start cutting back my distance the week before, and the week of I will do 2 or 3 3M runs, and then rest for 4 days before, and three or four days after. Right after a race, the worst thing you can do is just not move the rest of the day. You need to keep moving -- and this is true for the long training runs, too. Don't go crazy, but do keep upright, at least somewhat -- do laundry, grocery shop, go about the normal business of your day. Your muscles will thank you the next day -- oh! And don't forget lots of stretching. When I finish a Disney race, I get a massage, go back to my hotel and shower, eat whatever I want

! and then go to a park and slowly take in the attractions -- proudly wearing my medal!
Ok, sorry if that was TMI, but good luck with your 12M -- let us know how you do! Are you planning to use Gu or Bloks for your long distance? Anything 10M or over I do -- YMMV, but if you do think you will want something, you should try it out in the training runs so you can confidently use what helps you most on race day. I can't tolerate Gu, so I'm a Blok girl!
By the way, I knew absolutely nothing about race nutrition when I started -- I literally got the idea at the Expo before my first Half, and not knowing anything, decided I'd go with something I knew I could handle for the race. I ate Jelly Bellys -- which I really don't recommend!
Maria