To effectively cover the opening of your unused fireplace and reduce drafts, you have a few options. Using foam board insulation, like the one you mentioned, is a good choice as it provides excellent insulation and can help seal any gaps. It's also relatively environmentally friendly compared to other materials, as it can reduce energy loss.
If you prefer a more traditional approach, using plywood is also viable. Regular plywood painted with anti-mold and mildew paint can work well, but make sure it's sealed properly to prevent moisture issues. Pressure-treated plywood is more durable and resistant to moisture but is generally used for outdoor applications. Since your fireplace is indoors, regular plywood should suffice if adequately treated with paint.
In terms of cost, foam board insulation typically ranges from $0.50 to $1.50 per square foot, while plywood can range from $1 to $3 per square foot, depending on the thickness and quality.
Since you mentioned a gap in the flue, it might be wise to have a professional inspect it to ensure it's properly sealed. I recommend getting 2-3 local quotes on Handyman.com for the best options tailored to your needs.
— Assisted answer