There a several different ways to finish off a graphghan or photoghan - none of them are the right way. As I often say; the right way is the one that works for you. However, a lot of people have asked what I do so I'm going to share it here.
I back my graphghans with micro fleece because it's thinner and lighter than normal fleece. I like that it doesn't fray so it has the durability something like this will need.
I cut the holes in the fleece with a simple rotary cutter, and then crochet around the fleece. I then crochet around the blanket and finally crochet the two layers together using single crochet.
I think you'll agree its looks really smart. While you can get mirco fleece in an ever increasing array of colors; my advice would always to keep it smart and keep it simple. While a vibrant contrasting color might be fun now, it might not be to everyone's taste ten or twenty years down the line.
And to finish things off...