Design your own It's fuuunn!!!!!
And make sure they look pimp with blue red and green lights!

Basically, the 'Core' ships are very poor

I told know what the people at Stardock were thinking when they choose what to put on the CORE ships; they certainly were not think about SPEED!
You can design war ships better than the AI. Pick a weak AI target that is close to your borders and not allied to a strong AI. Look at what weapons and defenses that AI is using, research weapons and defenses to counter them, and then build that ship. Don't forget to include enough speed on your ships so that you can pick and choose your battles.

For some reason I have never seen the custom ship building area.

I'll look into that tonight when I get home.

Yeah, "Dude, Pimp my warships !!!" is the key to victory.

I told know what the people at Stardock were thinking when they choose what to put on the CORE ships; they certainly were not think about SPEED!

Does speed help in the battle or just getting to the battle? If it does how?

Speed is crucial for unarmed ships like Transports, especially if you can't spare an escort for them. It isn't really as important on Small or smaller maps, but it is hugely important for Gigantic (and Huge) galaxies where civilizations are dozens of parasecs apart.

One strategy, though, is to fill a Medium Hull (or even a Cargo Hull, if you don't intend to actually go to war) with weapons and defenses and nothing else, then park it at a world as a permanent defender. You can also do this with Sensors to make ships with huge sensor ranges.

A good strategy I use in almost all my games is to research up the Mass Driver Tree until I get NANORIPPERS (I think this is around Singularity Driver IV) -- one of the more powerful weapons in the game.

Then I design a small ship with 2 or 3 of these weapons, no engines, no shields and use these to defend my planets -- one or two per planet will protect them while I research up the Beam Weapon Tree and Engine Tree. Once I get some fast enough engines, I'll start designing ships to counter what my enemy is using.

Speed is indeed crucial in this game and I often keep my faster ships in starport until I see enemy transports within range. Then I will make some quick hit and run tactics to take the enemy transports out. Their fighters might go after my planets but with my Rippers in defense the best my opponent can hope for is a pyrrhic victory with heavy heavy losses. Seems to keep the balance in check until I can create some Medium Sized Cruisers and Capital Ships and begin my assault in earnest.

Have fun!

Funny. I never spend too much time making my ships look good.

I select a hull, double click engines, double click sensors, and then double click weapons and defenses... I often get a ship with weapons on the back and engines on the front and a sensor node hanging off the side... but I've seen some of those mod ships people have made -- great looking stuff...

For me it doesn't need to look pretty -- it just needs to get the job done.