Is it against Apple policy / guidelines to create a custom button that links to the App Store, or does it have to be the official App Store Badge?
I believe you can only use the official badge. See the App Store Marketing Guidelines:
Use only the App Store badge artwork provided by Apple.
Do not modify, angle, animate, rotate, or tilt the App Store badge. Do
not use the Apple logo alone. Do not use icons, logos, or graphics
from www.apple.com to promote your app. Do not refer to iOS in your
communications. Instead refer to the Apple products your app natively
The Download on the App Store badge must be legible on all marketing
communications in which you promote your app offered on the App Store.
For all online communications, you must provide a link to your app on
the App Store wherever the badge is used.