Large: Heavy and Command
Medium: Assault and Logistics
Small: Scout and Pilot

That's what I surmised, at least.
Thoughts on what this might forshadow as far as the "Specialist" suits? Many of them talk about combining traits of two of the base classes.

There are a lot more variations showing on the EVE item database:

http://eve.battleclinic.com/item/g351064-Infantry-Dropsuits-details.html

For instance, both the Atlas and Breach suits show variations. This suggests that the specialist (Tech 2?) suits will be based on far more than the types we see now.

Command was renamed crusader, which is Amarr. Pilot is Gallente.
Amarr already have a large frame (heavy), so crusader won't be a large frame.
Gallente already have a small frame (scout), so pilot won't be a small frame.

That's kind of what I was getting at, actually. I saw those suits a long while back on Buckingham. I would assume they would fit into the same size classes as the ones we have now

Well, no, that last DevBlog said we'll soon have the full range of suit classes for each Faction. That would mean that the Caldari will have Assault, Scout, Logistics, Heavy, Pilot, and Command suits just like the Minmatar, Gallente, and Amarr will.

Also, the name "Crusader" just doesn't make any sense to me, and honestly sounds kind of dumb.

I think you're misinterpreting something. What they did say was "We're hard at work expanding that list so that each race will will have one of each frame size that plays to their strengths and weaknesses", nothing about every dropsuit role being available for all races.
Can you show me your source?

I think you're reading a little too far into exactly what he said.

As an example, during the 2009 CCP Presents! where they first showed off Dust 514, the War Barge and MCC were introduced, at which point Torfi started referring to the MCC as both of those terms interchangeably unintentionally.

Look at it this way, for instance:
Four nations, all at war and developing immortal soldier technology. Only the Amarr develop Heavy suits and Command suits. Amarr are all about heavy armor, but why would only a single nation develop a suit designed to provide command support for squads? Isn't that something fairly important to anyone? Or why only the Gallente would develop a suit for pilots, or only the Minmatar would develop a suit for healing and supplying infantry?

It just doesn't make any sense when you look at it that way.

Or that we're so highly experimental and in testing (hence beta) that the nations are still trying to come out of thier normal warfighting mantras on the ground to deal with the new situations and needs yet?

I mean hell the republic just began standardizing thier equipment, a minmatar tank of yesteryear would have probably been something a dakka orc would have been proud of but you couldn't ask for another one like it.

Amarr slow powerful unstoppable will of god.
Gallente the select few proud, brave and elite.
Caldari all stand strong for the pride of the state.
Minmatar whatever allows me to bring fury and hope to my people.

This perfectly explains the suit mantra initial selections.

As for why the amarrians don't have tanks maybe what the caldari and gallente put out, outclasses previous tanks so much that the amarrians had to build new ones.

We have no idea how many 'bases' the game is going to wind up with. Hell in the future that number could be 24 base tech 1 suits and by all technicallity we have 8 right now the type 1 and type 2s.

As for each race needing it own skill I would also like to point out that every race did skin the cat a different way, and if you skin the cat wrong way with the wrong tool, the cat is going to tear you face off.

Amarr for example may have just thickened the armor and hardenend it, this requiring different subconcious training on the servos and muscle membranes of the suit vs a gallente armor tanking suit which is far more reliant on shape and resonance to defelct shots. Guy who trained nothing but amarr suits may be blowing out a servo on the gallente suit because he over exerted it to try to make the suit move instead of pacing it out for endurance of movement.

Crusader could be similar enough to the logistics so that the Amarr don't need to make their own logistics suit. This kind of thing could apply to all the new dropsuit so that despite significant differences, they can still perform general roles; this would make mirroring all the roles in each race unnecessary. Some races may not even need a particular role in their military for whatever reason.