The next ship you should make next is a toss up. If you want to explore the universe make a escort with six ion engines in it. I lovingly call it "explorer" (I never had much imagination with these sort of things). Or you can build another space station, this one with lots of weapons and armor on it(I general wait till I have tech level 2 to build this). If your sector has some nice super-terresteroid(s) in it you might want to build an escort with a outpost and one engine on it. I generally build an explorer, if you want my opinion. You didn't? Well tough. You should design all of these(for future use) and also design an escort with a space yard 1 on it and an engine.
While I'm on the subject of designing ships I'll give you some tips on designing. First every time you go up a tech level, go on a design spree. "Minas melanor" the bigger, the better is my motto. Make a better model of all of your existing ship designs and then make a few more.
There are are two types of attack ships that you can design, focused and combat. Focused ships are based on one type of weapon. The are great at its weapons speciality(like ripper beams are for up close range combat only but deal tremendous damage and mass driver cannons have a long range and deal a good amount of damage but take time to reload) but suck in all other types of combat. For this reason foucused ships need to be very fast(so they can get away or get close, depending on their weapon). Combat ships on the other hand have a litte of every thing with maybe a litte more of this than that. Combat ships have few weaknesses but on the other hand they have few strengths. Combat ships don't need to be very fast but, then again, its always good to be fast.