Backpacking Location 4 days 3 nights in VA

I am searching for a suitable location in Southern Virginia for a 3-4 day backpacking trip for my organization. We are planning to take 4 groups of 15 guys on separate trails, but all in the same area. We are looking for dispersed camping areas that allow fires, and don’t require a permit. Ideally we would like a loop trail with some mountain top experiences, water crossings, and a centralized location for a base camp for all groups. We also need a place that has enough water. We are trying to avoid areas that will be crowded. We are looking at doing the trip in mid-October, and then again in mid-April. Thank you in advance.

Backpacking in groups of 15 or more 6 hour vicinity of PittsburghSpoilerWilderness

I am looking for moderately challenging destinations with a mountain top experience for my church’s men’s backpacking trip. It is 4 days 3 nights. I am struggling to find places that you can go in groups of 16-18. Most places only allow groups of 10 or less.

I’m planning a August 3 day 2 night trip to Grand Teton NP and wanted to get some recommendations on gear. Sleeping bag, clothing items, etc. What am I not thinking about that you would suggest?