Well, since I've been playing WC4 pretty thoroughly...
"Friendly" Ships
Hellcat
Good speed and manoeuvrability, decent missile loadout, good guns... I can understand why Confed has so many of those, even though it's by no means an awesome fighter.
Longbow
A bomber. That means very powerful guns, a VERY good missile loadout, and a rear turret. It also means lousy speed and manoeuvrability. As long as you keep a finger on the decoy button and you carefully manage your missiles, it's a better fighter than it may seem at first.
Banshee
Very good speed and manoeuvrability (well, it's a light fighter), good missile loadout (8 missiles). The lasers don't do that much damage, but they don't use much energy and they fire very fast. If you put a bit more power to the weapons, you won't have to worry too much about running out of energy. The Scatter Gun is quite good, but you'll probably need to get fairly close to use it. It's especially useful against big targets.
Vindicator
An interesting ship. Speed and manoeuvrability are not that good. The regular guns are quite good, but they may require some more power to be really useful (mainly due to the Tachyon Cannon). The Stormfire Cannon is very good, and you can set your guns' power to 0 (since the Stormfire Cannon doesn't use energy) as long as you have some ammo left. You might want to put a bit more power into the engines as well, since more manoeuvrabilty definetely helps when flying the Vindicator.
Avenger
Good missile loadout, powerful rear turret, poor speed and manoeuvrability, powerful frontal guns, good shields and armor. It's not that bad a fighter, but I usually only pick this ship if the game forces me to, since I don't like dogfighting in the Avenger (it tends to get hit a bit too easily for my taste). Fortunately, it has a Stormfire Cannon.
Dragon
Very good shields and armor, extremely powerful guns, decent speed and manoeuvrabilty, good missile loadout, infinite afterburner, cloaking ability.
While the regular guns are very powerful, they use a lot of energy. Therefore, I tend to use the Plasma Cannon most of the time, and I only use Full Guns when I'm sure to have a good chance of hitting my target. The Fission Cannon is extremely powerful, but it requires some time to charge it up and aim, so it's mostly useful against big targets like Longbows. Overall it's a pretty powerful fighter, but fans of fast fighters will most likely like the Bearcat best.
Bearcat
This is probably my favorite WC4 fighter. Fastest friendly ship in the game, good shields and armor, very powerful guns (4 Tachyon Cannons), good missile loadout (8 missiles, same as the Banshee). I strongly recommend putting more power into the guns so you can see the Bearcat's full potential. I tend to fully deactivate the repair systems most of the time, repairing only between Nav points (if necessary). I sometimes very slightly lower power to the engines and shields, since the Bearcat is so good at dodging and needs more gun energy. The 4 Tachyons are really good, get pretty close and blast 'em. Now that I'm used to flying the Bearcat, I can beat Outrun Ella easily, even the Cruiser.
TCS Lexington (Concordia class)
You don't really need to try to protect it... Unless you want to lose the game, that is.
Transport
Despite the fact that it could be easily destroyed, the one one-hit missile kill feature makes WC4 escort missions pretty easy. Okay, so you do have to watch out for those Capship missiles in one mission. I recommend taking the Vindicator.
Shuttle
Like the Transport, it could be easily destroyed (hint : the keyword is "could").
BWS Intrepid (Durango Class. The BWS Tango is pretty much safe.)
The Intrepid can usually take care of itself... Except in Outrun Ella. For the last two Nav points, I strongly recommend telling your wingman to attack the Longbows while you take care of most dangerous fighters (Hellcat Aces, Bearcats). Of course, you can try to help your wingman destroy the Longbows when you're sure not to get hit too much (i.e., I recommend destroying at least one Bearcat and at least one or two Hellcats first). And pick a good wingman, like Hawk.
Frigate
If you've ever seen one of those blow up, you tell me.
Dralthi
You don't get to fight with them much, but they seem to be decent fighters.
Kilrathi Starbase
See Frigate.
TCS St. Helens (Supercarrier)
It's big, it's powerful, it's the twin to the Vesuvius, it's invincible.
"Enemy" Ships
Razor
They're easily destroyed and don't have much firepower... But watch out for those missiles. They're usually not that much of a threat except in the Circe Search and Destroy mission, where they really have to be taken out as soon as possible.
Arrow
They're very fast, and somewhat hard to hit, but they still have the weaknesses of light fighters : poor shields and armor, and not that much firepower. Some Arrows can cloak as well, but usually they aren't that dangerous (I do remember them being somewhat tough in a Selenos mission, but that's about it).
Thunderbolt
It's big, it's slow, and its rear turret won't prevent it from getting blasted to pieces. Watch out for the FF missiles and they shouldn't be much trouble.
Banshee
Quite dangerous due to their sheer speed, manoeuvrability, firing rate, and missiles. Fortunately they aren't very hard to hit and they're armored like the light fighters they are.
Vindicator
The guns can do decent damage, the rear turret can be annoying but isn't very dangerous. They should fall fairly quickly, just remember to let your guns recharge and avoid the missiles.
Ground Turret
Take it out as soon as you can, preferably with guns, or you won't last long.
Hellcat
Confed's favorite fighter, apparently. While they're not very difficult to destroy, their firepower can make them quite dangerous in groups, especially if an Ace is among them.
Mine Turret
They can be somewhat annoying if there are many of them, and they're decently armored, but that's about it. They really don't do much damage.
Excalibur
They can do quite a bit damage. Fortunately, they tend to be easy to hit. Given how powerful they were in WC3, they're not as dangerous as you might expect, but do avoid their hits.
Bearcat
Very fast, quite manoeuvrable, pretty powerful, very tough, very nasty. Use missiles if possible. If not, just get close and use powerful weapons.
TCS Lexington (Concordia class)
Easily destroyed, no matter whether you intend to leech it or blast it.
Transport
Pitifully easy to destroy.
Jammer
It can cloak. It's still a transport. Two dumbfires and a few hits should easily settle the problem.
Frigate
It's tougher than the Transport. It's still fairly easy to destroy.
Destroyer
More powerful than the Frigate. If you can afford to use a few IR missiles, it'll be very easy. Otherwise, just avoid most of its hits and it shouldn't be too difficult.
Cruiser
Actually a bit difficult if you can't afford to use any missiles or torpedoes. Just avoid its hits as best you can when attacking it. You'll most likely have to go evasive a few times. In case you're interested, four leech missiles should be enough to disable one.
Black Lance Transport
It's quite a sight, but it's a lot less tough than it seems. It's easily disabled, and two torpedoes are enough to destroy it.
Axius Starbase
It's invincible, so don't waste your time attacking it.
TCS Vesuvius (Supercarrier)
Invincible until you're explicitly told to destroy it. A few dumbfires or the Flashpack inside the Hangar will take care of it. If you use conventional weapons, be sure to be fairly close to the Hangar's exit when you are inside the ship, and get out immediately after the Vesuvius sends its Mayday comm message.
Ella (Superbase)
I'll admit I haven't tried too hard to destroy it without the Flashpack, but it seems to be tough. If you do use the Flashpack it's a one-hit kill.
Starbase
Two torpedoes is all it takes to destroy the Starbase.
Comm Station
It can't defend itself, and I'm only mentioning it because it takes many hits to destroy it.
EDIT : I forgot the Tanks... The Hover Tanks are helpless but do have to be destroy quickly, and the Missile Tank appears to be the most dangerous (but it can still be destroyed last).