Here's some further information for you, Say_my_name. There's a nearly infinite number of possible combinations, but certain template designs tend to perform well.
Fighter: Small hull, with one beam weapon. These are useful in the early game for chasing away colony ships, and sometimes later on if you don't have any up-to-date beam weapons. You'll need hundreds (if not thousands) of these to accomplish something significant, however.
Missle Boat: Medium hull, one 5-rack of your best missile weapon. Use the extra space to add good computers and manuverability. Missile weapons are too large to fit on Small hulls, and it's generally not a good idea to put them on Large or Huge designs (better to get more total missiles into the fight by using a Medium hull). Very useful for raiding and conducting hit-and-run attacks. On the lower difficulties, where the AIs don't have high numbers of bases/shields, you can conquer entire maps with these ships.
Gunboat: Large or Huge hull, packing as many of your best beam weapon as possible. These ships are intended to defend your colonies or recent conquests against AI fleets before you get the chance to stand up missile bases. These are usually too expensive to build in the early game, but increasingly come into their own in the mid- to late-game. Autorepair special is a huge plus for these ships.
Bomber: Small hull, equipped with a single bomb (Fusion in the early game, later Antimatter/Omega-V). Make sure to maximize combat speed, and any computers you can fit on. Build these by the thousands, and use them to punch through the AI defenses. Sometimes you can't fit a bomb on a Small hull, so I've had success with multiple Omega-Vs on a Medium hull as well (although this is less ideal). Late in the game, you can also often dispense with the speciality bomber by sticking a couple dozen bombs onto a Huge Gunboat design.
Speciality ship: A design created for one specific purpose, usually to counter an AI threat. A Repulsor ship with 2-space beam weapons, a Warp Dissipator ship to freeze unbeatable AI stacks, or an Ion Stream Projector design to counter a giant stack of Small ships would all be examples. There's no guidelines for this category, you'll just have to get a feel through experience.
That's essentially it. Virtually all of my ships are a modification of one of these five designs. Here's an example:
The Merculite and Pulson designs are both Missile Boats. You also see three different generations of my Gunboat ship, starting with lasers and ending with Fusion Beams. I didn't use a speciality bomber in this game because I had the Autorepair special, plus FIVE Rich worlds, and thus built a lot of Huge ships.
Another example:
The Huge and Huger designs are both lategame Gunboats. The Stinger design is a Missile Boat, and the Bomber design is a (what else?) Bomber, which had to be on a Medium hull because the Omega-V wouldn't fit on a Small.
Anyway, as you play around with this stuff you'll get better. Good luck!