What service would the more experienced out there recommend run this on? AWS seems rather expensive, but Digital Ocean wouldn't provide much storage space. Also, what about reliability? Any advice on not getting blacklisted for sharing a subnet with spammers? Or do people generally run setup like this old school: on a server in their bedroom?
TransIP offers VPS with SSD at comparable prices to DO, and more disk space. It's also not an US company, if that makes any difference. No affiliation, just a happy customer.
Regarding blacklists, I run my outbound email through Mandrill. I know it cuts down on the privacy aspect, but I send very few emails anyway compared to what I receive.
Why would users need to store all old mail on server? You can auto archive it or simply delete about 95% of mail which you won't ever need later again.