Jill, this is an okay stretch for an inexperienced hiker. The hiking is moderate as far as the AT goes, however, their is a section called the “roller coaster” lots of needles ups and downs just north of Linden. I’ve hiked that area extensively as I used to live in the D.C. area. I am uncertain why you are dead set on that are as you might consider Front Royal south to Waynesboro instead. This would entirely be in the Shenandoah National Park and is a very nice hike in general and a great hike for somebody getting into long distance hiking, in that region I couldn’t reccomend it more.
The weather should be very pleasant that time of year, a 40 degree bad would probably be adequate. You may want to average 10-15 miles a day, this would be easier in the SNP, which is much more smoothly graded. If you did the SNP, food access would be easy as the SNP has lots of waysides open that time of the year. The data book would probably be sufficient, maybe the maps (i love the maps) and perhaps the relevant ATLDHA books pages. Have fun.
Va Hiker