Hello Charles,

CS> I'm very curious about the 'Pi', I'm curious, is there a built in
CS> graphics card,

Not a card, but it is on board HDMI and Composite Video on ALL Pi models.
Many people use Pi's headless via SSH from another machine.
After installing software, immediately change the "default is your fault"
Password, when the machine is connected to the InterNet.
Otherwise it can be hacked very easy.

CS> or is there some sort of device needed for video?

No.

CS> I Noticed there are a few USB ports,

Yes 4 USB2A type.

CS> networking ports on a few I've read about.

On all Pi Model B's there is a RJ45 EtherNet port at 10/100 Mbit,
and at the Pi 3B+ you can use 300 MBit max at that port, not GigaBit.
The Pi 3B and 3B+ also have WiFi.
The 3B only 2.4 GHz, but the new 3B+ also 5 GHz.
The A models and the Zero do not have enought connections for your task.

CS> These little systems seem pretty neat,
CS> as I'm thinking about moving my BBS off of a 'big' box onto a PI system,
CS> Looks 'cheap' and easy to maintain too.

That is possible for sure.
It also consumes less power, a big advantage when using 24/7.
My FidoNet host in the Netherlands 2:280/5006, Kees van Eeten is using
several Pi's for FidoNet under Linux with BinkP protocol,
both in IPv4 and IPv6 !

In the Netherlands and Belgium we have a Big Ben Club at 7 locations each month
getting together with all kind of Pi's.
Look at:
        RISC OS and Linux in Mortsel near Antwerp.
    RISC OS and Linux at 7 locations in NL.
      Linux in Mortsel near Antwerp.
                              Every 4th friday of every month.
                              You missed the yesterday one ;-).

And when you want to start up it your self, donot use NOOBS,
but install the Raspbian Linux or Ubuntu.
NOOBS is a nice try to feel the os, but all versions on it are incomplete!
So for production systems use a much better version.
Good luck.

Henri.

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