Each race has a "fast" hauler and a "large" hauler. The latter aren't as useful as they may seem, they are only good for hauling large but low value cargo. To haul any seriously valuable cargo you need a ship that can fit a 10mn MWD so you can perform the maneuver "MWD cloak trick" (if you don't what that is google it). To fit a MWD on any of the "large" haulers requires giving up so many slots to powergrid increasing gear you wind up with less cargo space than a "fast" hauler which has plenty of grid to fit a MWD to start with. Since the "fast" haulers also accelerate to warp faster fitting the 'large' haulers for MWD cloak is pointless. The specialist haulers do have to fit some grid increasing gear to fit a MWD, but losing slots doesn't affect cargo space the way it does for the "large" hauler group, since their special holds were never affected by cargo expander modules or rigs in the first place.

As far as race goes, I recommend taking the long view and thinking about what T2 haulers you would like to fly. You might train Gallente to level 3 or so to use their specialist T1 haulers, but you should only train a racial industrial skill to 5 if you plan on flying that race's T2 haulers. Personally I favor the minmatar haulers for the very simple reason they are quickest accelerating to warp. There is no better way to avoid being ganked than to simply get to warp before the potential ganker can react.

So, it seems like I would want to get a fast hauler and equip a MWD
on it, so what would be the "fast hauler" for each race?

What are you going to do with this hauler to make ISK?

Elena mentioned it above, and I think it is important to note. Courier contracts will normally require a large hold and/or high collateral. Are you using this for trade?

I'm just going to be using this ship for trading.

The first fit here:
https://forums.eveonline.com/default.aspx?g=posts&m=5261708#post5261708
is quite good (even in low-sec) provided you pay attention to what you do and have dock/undock bookmarks. Also has a good warp speed and looks nice. Not much skills required.

Hauling will not give you much ISK.

Best blockade runner for the beginner is Wreathe with MWD and cloak. Learn how to do the MWD/cloak trick and you will be able to by pass many gate camps. I use something like this:
[Wreathe, ErgoDron]
Inertial Stabilizers II
Inertial Stabilizers II
Expanded Cargohold II
Expanded Cargohold II
Expanded Cargohold II

Experimental 10MN Microwarpdrive I
Adaptive Invulnerability Field II
Adaptive Invulnerability Field II
Medium Shield Extender II
Medium Shield Extender II

Improved Cloaking Device II
Core Probe Launcher I, Core Scanner Probe I

Medium Polycarbon Engine Housing I
Medium Cargohold Optimization I
Medium Cargohold Optimization I

Giant Secure Container
Giant Secure Container
Giant Secure Container

Very soft target for me.
Don't use active hards they are worthless against alpha ships.
Where is damage control?
It can save you if someone will not be using a tornado.
ps. LSE is a must.

Thrasher/Catalyst with cargo expanders. Works only in highsec.