I recommend you find a friend, or friend of a friend who does sys admin work at a company or school, who uses Linux and one of the common MTAs -- sendmail, exim, postfix. Pay them a flat monthly fee to handle your email, and do whatever they tell you, get a VPS or hosted service or linux machine on a cable modem or whatever. Pay them until you can afford to have a "real" setup, and in the meantime focus on making your startup work.
Personally, I would put a light weight (cpu and bandwidth will be minimal) linux server on whatever is the cheapest way you can get a business class fixed IP. I use exim.
When olefoo said keep the MTA and web operations separate, and you asked "with a queue?", I think olefoo meant keep them on separate servers. The MTA and web operations are normally separate daemons that run, and the web submits an outgoing mail to a queue in the MTA, but it's not somethingk you have to write or set up, it's the default way an MTA works.
When olefoo mentioned keeping incoming and outgoing MTAs separate, that might be a good idea but I would warn that if your account notification email comes from a different IP address than is listed in your MX record, some of those emails won't get to users because they will be blocked, dropped, or spam-foldered.
Once you start having to deliver lots of email, you will find that there is an incredible amount of pain in doing it reliably. You have to regularly examine all your bounces, and check for successful delivery to test accounts at the big places such as yahoo, gmail, and hotmail. First, you will have to make sure your From: and other headers are configured exactly correctly. Get a reverse DNS record correctly set up. You will probably have to learn about SPF records and domain keys and stuff like that. It can be a chore.
I still have problems with it. I have fixed IP addresses from a business class Time Warner connection, and I have had those IPs for a couple of years now, and some spam block lists still list me as "dynamic" ips, even though I have been through the removal process over and over. I have given up on ever being able to deliver mail reliably to earthlink addresses.