Hello Maximillian and welcome to the guild. As for software I think try out all of the free ones first and get a general sense of what works for you....
Not sure if that means your requesting a commission or replying to service them but in the latter case I would recommend posting up previous maps and...
Ohhh... so cool. I love it. very Tribal. Also reminds me of the Isle of Dread adventure module... the island shape.... Can't wait to see the finished...