I believe postfix is the default mail server in ubuntu. You will need to install and configure postfix (which is not hard). You will probably also want to install some form of spam filtering, for that I would recommend
Maia Mailguard. It can be a bit of a task to install, but the results are well worth the effort.
While you don't need to run a DNS server in house, you will need to have a domain name registered and you will need to have DNS set up (specifically MX records) to successfully receive e-mails. If you want to have a mail server that will deliver mail successfully, especially to yahoo, hotmail . . . you will want to add
DKIM and
Sender Policy Framework to your setup as well.
You will need a fixed IP address, unless you use a special configuration and have another mail server spool and hold your incoming mail and send your outgoing mail (which would for the most part do away with the advantages of an in house mail server).
Good Luck