Which one would you recommend for simple, secure setup, DoveCot or PostFix?

For beginners, definitely DoveCot. As you'll notice with PostFix, it has many many more configuration options. You can try both, even. But for you, I recommend DoveCot.

DoveCot includes IMAP and SMTP right?

DoveCot has IMAP but you will need to find another authentication daemon for SMTP. PostFix is a good choice for it, tutorial here: exratione.com/2012/05/….

Will hostname mail.example.com mess with apache2 at all?

Not at all; your DNS records are set on the domain's name servers (or your DNS server if you operate one). They simply resolve domain names into IP addresses which allows people and computers both to find your server. Your Apache server wouldn't even know that there is another subdomain.

That tutorial looks good, I'll try it in a second, but it has nothing in it about DNS records. What CNAME's should I change and should I change the MX's?

Woah this chat is cool

You should first read how mail delivery works; CNAME records would be added of your choice (mail.domain.com or smtp.domain.com etc.) And you'd likely want to use A-Records since you should already be using an IP address that does not change. Dynamic IPs can complicate some mail delivery if it changes but the DNS record is cached elsewhere. Your MX records will be only for if you want to use mail on your domain (receiving mail).

I want to be able to set up email to my server from the mail app on my computer from a remote host, like when you set up gmail you use imap.google.com and smtp.google.com

And what do you mean if I want to use mail on my domain?

And why would I use A-records? Wouldn't I just make an a record "@ 123.456.789.123" and then cname records like "mail @"

Because the server you use to send mail does not require any modifications to your domain, whereas you need to set up records to receive mail on your domain. I was only suggesting to use A-records for your mail subdomain because you should give it a static IP and it will also save a few fractions of a second of lookup time. Instead of resolving mail >> subdomain >> IP, it would go mail >> IP.

So I should set my MX entry to "0 @ mail.mysite.com"

You'd want to set your mail server up FIRST.

Does it make a difference which order I do those in?

Hey are you still there?

got a quick question

ok