It's compatible with 14.04 — that's actually the recommended distro to use for Ubuntu, though there will be really no difference using a different version. You'll need to set it up on a new droplet if you're not entirely sure what you're doing, but after the initial set up you can go ahead and add the packages you need for your apps. Keep in mind that you'll need at least 1GB memory, so that's the $10 droplet. Additionally, if you're unable to modify your configs to work in conjunction with your web apps and mail server, it may be best to use two different droplets; one for your apps and one mail server. It'll make things a lot less confusing.
iRedMail comes fully ready-to-go other than a couple of minor things you need to do for DNS, and the default settings are only suitable for the amount of memory it recommends, so unless you're able to change configs to suit your needs, don't go with the 512MB droplet.
To answer a couple of your other questions:
1) Your MX and A records can be added through DigitalOcean. You would do something like: mail.example.com., as an A record point to your mail server's IP address (your droplet's IP). MX would be mail.example.com. and the priority can be anything, but people generally use 5.
2) You can change your droplet's host name by doing,
# sudo nano /etc/hostname
# sudo nano /etc/hosts
127.0.0.1 mail.example.com mail localhost localhost.localdomain
The above is detailed in the iRedMail documentation.
You can use any host name you want to, but you'll likely just want to use "mail." It doesn't matter what it is, as long as it's added in your DNS and points to your mail server IP address.