The DPI you need depends on how far away you want to view it. If your spreading it out on a table and look at it like you would look at any other page or book then 200+ is what you need. As a poster tho you can go less.

From a tech point of view images much bigger than 14K start to get unwieldy. Some image file formats can start to have issues at 16K but you would most likely see it slow down a lot. BMP and PNG seem ok at 14K but past 20K its iffy.

I deal with images up to about 14K. I would probably have tiled it before then tho. Maybe at 4K squares or 8K squares. So you could do a map as 4 squares of 8K x 8K. You just have to ensure that the overlap is seamless.

I have the main MeDem map at 20K square which is 10x10 of 2K tiles. This map is not entirely manually made tho.