Email Processing Service

I am looking into starting an email processing service, and I am
looking for email hosting services. I was hoping one of you could
point me in the right direction. Technical suggestions and criticisms
are welcome as well.

The basic idea is as following:

1) User sends an email to "process+parameter@myservice.com"
2) My service has a server S, which periodically downloads all
messages sent to any address @myservice.com, processes the messages,
and creates new email messages based on the user's message.
3) My service sends these new messages back to the original user.

My expertise is in the specific processing I am planning for the
email, so I am new to email hosting services.
The requirements that I think I will need are:
~1GB of mailbox storage (the messages will have attachments, so space
will be filled up quickly)
~Ability to handle 1000s of messages a day, and 1GB of transfers a
day.
~Ability to use my own domain name or register one through the service
~Relatively cheap (This is likely going to be a free service, so I
want to minimise the drain on my wallet)

Some of the options that I have looked at for hosting seem close to
what I want. For example, GoDaddy runs a service that fits most of
what I need for $20 a year, but limit SMTP relays to 250 per day
(unless you pay exorbitant oversend fees). fastmail.fm runs an
extended service which looks promising, but has a 1GB/month transfer
quota. Easyspace has a basic package, that seems good, but has a
mailbox space limit of 100MB.

Any thoughts?

Eli Gibson