Yeah, I am playing the Dread Lords campaign.  If the more advanced ships aren't allowed in the first mission, how am I supposed to get through the opponent's heavier ships and take the planet?  They simply shoot down my transport ships before they can get to the planet.

I did some checking, and the tutorials do cover these topics. You want to look at the one named "Ship Designs", but watching "Managing ship Designs" is helpful too (it also listed before "Ship Designs" tutorial). You might want to watch them all if you are still learning the game.

You can find the tutorials as a button on the main menu (after intro videos play or are skipped).

Note that later versions of the game have changed some details or made changes to the User Interface, but it should be easy to figure things out. If you have any further questions, feel frees to ask.

I am playing Galactic Civilizations 2 original release.  So am I to understand that the player is expected to only build their own ships and never use the stock ones supplied by the game?

Yeah, the pre-designed ships in Dread Lords don't take full advantage of all the technologies you have. Take for instance the miniaturization techs. They increase the space possible on your ships, so you can stuff more weapons and defenses on your ships. Normally, a civilization can get as high as 100% miniaturization (that much will double ship's capacity) by researching techs alone. Suffice to say, a ship with twice the gear is likely to beat a ship that has to make due with the normal space allocations.

So yeah, designing your own ships were the norm. If you don't want to design your own ships, you could play the latest versions of the expansions, both of which has an AI ship designer (the original game was too different from the expansions to easily port this feature back to it). I find the AI ship designer to be sufficient for my needs (keep in mind that it can't design anything fancy like constructors or ships that use atlas modules). The first expansion, Dark Avatar, is the one most similar to Dread Lords, if you care about such details.

You can also play the older campaigns in the expansions, so Twilight of the Arnor can play the both Dread Lords and Dark Avatar campaigns (but must do so using the new tech trees and other new features).

Edit: The stock ships are likely stuff from GalCiv 1. In that game, you couldn't design your own ships so they supplied you with what you needed. If you played the original, you will likely notice things that were carried over from GalCiv 1 to GalCiv 2. I think even the original release of GalCiv 2 I bought in stores had different ability stats you could select before the game begun than they do now (which if memory serves, looked identical to what you had in GalCiv 1). So yeah, those ships probably had a purpose in a different game.