Select the various techs that you research. Many will give a list of what you need for a certain ship.

Example: Open "Research Screen" and click on "Sensors IV." One entry in the information box will be NEW SHIPS, with the entry "SURVEY SHIP--4 techs needed" and a list of the techs.

Many techs will have lists of ships like this. If you want to see most or all of them, try looking at the various propulsion techs, as most ships need certain engines. This will give you a list of ships and what you need for them; just research the other requirements and the ships will appear under "All" and "Core" in your Shipyard.

Edit: Yes, but doesn't the AI base its designs off of the defaults he's looking for?

If I had ever seen a default ship that was even half as good as I could build with the same technology, I might pay attention to them. It's like they only fill up half the available space. Two-speed colony ships, indeed.

Ahhhh... Found it in the Galactopedia thread. There's a program there that lets you see the components and required tech for each of the starships.

And they suck... Really. No defense on a lot of those ships? It's a straight slugging match: "I shoot, you die! You shoot, I die! How many ships do you have left? Okay, I shoot again! Hah hah!"

Rather than use the core ships create new designs based on your current technology. The core ships are very slow; you'll want at least a warp engine on your attack vessels and by mid-late game on a very large maps you'll want two hyper-warpIII engines. Speed is critical to attack fleets even with the first strike advantage going away in v1.2!