You’re in for a fun and scenic hike! The easiest way to the NCT from Traverse City is to take the Traverse City to Kalkaska Trail to the NCT in the Sand Lakes Quiet Area.
http://www.northcountrytrail.org/gtr/TC%20to%20Kalkaska%20Brochure%20map.pdf
http://www.northcountrytrail.org/gtr/TC%20to%20Kalkaska%20Brochure%20front.pdf
Heading south, it’s about 200 miles to Croton Dam where the trail mainly hits the roads. You’d still get quite a bit more than just the Manistee National Forest with additional highlights including the area surrounding the Boardman River, fantastic new trail by Fife Lake, some of the finest hiking on the Manistee River with Highbanks Rollway, and Hodenpyl Dam Pond.
A couple worthwhile alternates: take the Manistee River Trail on the east side of the river crossing the mini-mac bridge, and also Loda Lake Wildflower Sanctuary and the NCTA schoolhouse.
From Croton you may be able to arrange a ride or get a good idea for options by contacting the Western Michigan Chapter of the NCTA: http://www.northcountrytrail.org/wmi/index.php
I recently purchased a book that I highly recommend: http://www.amazon.com/Hikes-Michigan-Wisconsins-Country-Explorers/dp/1581572255/ref=pd_sim_14_3?ie=UTF8&dpID=51aDQ4f7VRL&dpSrc=sims&preST=_AC_UL480_SR318%2C480_&refRID=0SBAR9Z71E6B2YV9KKMX
Here is a data sheet that is still quite accurate for the Manistee National Forest:
http://hereinthewoodsalso.weebly.com/uploads/1/5/5/9/15591998/water_available_w_mi_spw.pdf
I found the ArcGIS map on the NCTA website to be a great resource and also the individual chapter pages.
You may also find some trip reports helpful. Here’s a link to my NCT page: http://ericshikes.blogspot.com/p/north-country-trail.html
Hopefully that’s a good start :) Let me know if you have any other questions.