You'll miss out on some worldbuilding, but Butcher writes them in a way that (until a certain point) you should be able to follow the core story of the book wherever you start: personally, I'd recommend starting at either book 3 or 7, as 3 is where he first starts building the foundations of an overarching storyline, and 7 was deliberately written in a way that anyone could jump in. Five's decent enough for a start.
I think three is particularly important because the stuff that happens has a profound effect on Dresden mentally, and if someone really felt the need to skip books I would say to start there.
Thanks to Linklele for my new avatar!
If i had superpowers. I would go to conventions dressed as myself, and see if i got complimented on my authenticity.