Trying to run a server on a static IP from my house, DNS questions

[Xn Nooby]

I am confused about how to set up my DNS information for my server.

I bought a static IP address from Verizon, and registered a domain
name at GoDaddy.com.  My Ubuntu 8.04 server is connected to the
Westell DSL router that Verizon sent me.  My goal is to run my own
Linux server, so that I can learn more about linux system
administration.

My first step was to configure the "A" record at GoDaddy, and get it
to point to my static IP, which worked.  I can enter
"www.mydomain.com" and it forwarded to my IP, through the Westell
router, and to my linux box (which is running Apache). That works.

My second step was to configure the "MX" record at GoDaddy, that is
when I started to get really confused. At one point I had it working,
by creating another "A" record that pointed directly to my linux boxs
full name (server.mydomain.com), and then telling the MX record to use
the same name (server.mydomain.com).

I wanted to configure my mail the "correct" way, so I tried to use
GoDaddy's "@" symbol. I deleted the "A" record with my servers name,
and created a CNAME record called "smtp" that pointed to "@". Then I
configured the MX record to use host "@" that goes to "smtp". It looks
right, but email doesn't work now. The records look like this:

A Records
Host   Points to
@      1.2.3.4

CNAME
Host  Points to
smtp  @

MX (Mail Exchange)
Priority  Host  Goes To
0         @     smtp

So I called GoDaddy to find out why my mail didn't work, and was very
surprised at the answer.

The Support person said since GoDaddy wasn't hosting my server, I
needed to update the DNS server of the company that was hosting my
server - apparently, me.  He showed me the GoDaddy option in their
Control Panel where you set your "Name Servers", and said I should
probably put the Verizon DNS values there. So now I think I need to
call verizon to see if I can update my DNS values in their servers.

I asked the GoDaddy support how I was able to browse to my website if
they weren't my DNS server, and he said it was probably luck, and it
wasn't guaranteed to keep working. Which seemed plausible enough,
though strange.

While I was on the phone, it occurred to me, since my goal was to
learn linux administration, maybe I should run my own DNS server
alongside my webserver and mailserver. Which makes me wonder, do I
even need GoDaddy?

I suspect a lot of people are also running linux servers out of their
house on static IP's, so I thought I would ask how others are doing
it.

Any suggestions?