Problems with your request:
a) Almost no host will allow storage of so many images. Any one of them will kill your site immediately if they find out that you are abusing their offer and hosting a "HUGE photo gallery" as you claim.
b) If you're hoping to use this host as file storage, using the images on a different server, think again. Hotlinking is illegal. I apologize if I am on the wrong trail here, but because you don't mind "thousands" of pop-ups, I'm guessing that you aren't actually going to actually use the space for HTML pages.
c) "Unlimited" bandwidth does not exist. First, the word is "data transfer", not "bandwidth". Next, "unlimited" does not exist. Please give us a specific number of MB or GB that you are looking for.
d) Very few hosts offer 100 MB or more. The ones that do often have very strict limits imposed. Some do not offer FTP, and I don't think there is any that allows file storage...
I don't think a host exists to fulfill your demands.