Defending: at least 1 medium hull with decent weapons on each planet. Though this is not absolutely necessary, I prefer this to having to constantly look out for sneaky attacks on any of my planets; besides I usually produce many of those ships in the mid-game to keep my military rating up, until I get access to better weapons.
For my border planets: multiple of those or stronger ships. Also at least 1 ship with a few points of attack and plenty of speed (at least 5 pc) which I'll use to intercept enemy troop transports

Attacking: either around 3 medium/large hulls with plenty of attack or (if I'm really stomping the enemy) a fleet consisting of 1 spore ship and 2 medium/large hulls. You could do the same with transports though in many cases you'd need more than 1 transport.

In the beginning of the game I don't really have fleets yet, just dispersed ships for defense and in case I have a spin control center, plenty of ships in orbit around that planet.
In the late game I will have similar fleets but access to better weapons (at least 60 attack) and large or huge hulls. With those I rarely need to stack more than 3 ships in a single fleet.

It really depends a lot on the game. Generally, I use a mixture of the two biggest hull sizes I have for most fleets, although I almost never use tiny hulls and I rarely get Massive Scale Building unless an AI does, so in practice this means small/medium fleets early on and large/medium fleets later on. I tend to have 4 basic ship roles for medium and larger ships:

• Planetary defender - no engines, no life support, lots of weapons and defenses. Occasionally supplemented by small defenders, though I rarely create specialized ships with smaller then medium hulls.
• Fast ship - best engines (obviously), extra life support, typically has a survey module, heavier defenses then weapons. This tends to be used for exploration, and when I'm not facing a military threat, I have most of them on auto-survey. I stick at least one in each fleet for the sensor boost.
• Heavy hitter - smaller engine then the fast ship, best weapons and defenses. Pretty much exactly what it sounds like. This makes up the majority of my fleet.
• Command ship (in TA only) - gets whatever fleet modules I have available. Usually only one to a fleet. Sometimes unarmed, but I frequently put a single weapon and tons of defense on it so that it can soak up enemy fire, since they'll target it first.

Occasionally, when playing with one of the civilizations that gets speed-boosting fleet modules, I'll create "carrier groups" consisting of a large or huge hull with a speed module, one weapon, and tons of defense, and lots of tiny/small fighters with nothing but weapons and life support, as well as occasionally other big ships thrown in there. The "carrier" lets me skip engines on the fighters so they can get more weapons, and takes the hits for them in battle so I don't constantly have to replace them (which means I don't have to give them defenses either).

Again, though, it really depends on the particular circumstances of the game. I'm playing two games on TA right now - one as the Krynn and one as the Torians. As the Krynn, my primary antagonist has been the Drengin (though we're at peace now and they're falling apart thanks to a horrible economy, and the Torians and remaining ex-Korath pirates are much bigger threats). They're using beams primarily, but they had lots of Dominator Corvettes, so I designed a specialized "Corvette Killer" medium ship with armor instead of shields to deal with those.

Meanwhile as the Torians, the Dread Lords have invaded, so I'm designed anti-Dread Lord forces consisting of 1 Lucky Ranger, of which I've found about 6; 2-3 medium "Attack Cruisers" (the heavy hitter archetype above); and tons of tiny "Kamikaze" fighters - basically a bunch of mass drivers strapped on an engine. It's working pretty well - I can take down a Dread Lord fleet while losing just the Kamikazes, which can be built once a week by my best planets - but I would never be using this formation in normal circumstances, which again goes to show how much of my fleet design depends on the game.

I haven't gotten above 'tough' in difficulty, but at my level: 

I never spend resources fortifying planets.  I tend to play huge and above galaxies and the number of ships to fortify versus the resources to build mobile offense-defense fleets doesn't make sense.  Ships are for fighting -- and deterrence until you're ready to fight.  Fleets sitting in orbit and not fighting are a waste. 

If I can beg, borrow, steal, or con warp bubbles out of an enemy -- and I'll trade drive tech to the Terrans to get them to make it -- then my command ships (usually class-named Delicate Harmony) have warp bubbles, two top-tier engines, one Laser V, and as much type-specific level 2-3 defense as will fit in the remaining space on a medium hull.  If no warp bubbles then some other module, but one fast fleet is as good as two slow ones. 

To the command ship I add two firepower ships; two good engines, one or two defense modules, and whatever firepower I'm using -- usually whatever nobody else is using, and I manipulate this, too, trading one good weapon type to everyone while researching another line.  This is the Dire Radiance class of mediums. 

That's my basic offensive-defensive fleet.  It has tremendous resilience, I rarely lose one, and typically don't need anything more advanced, though I do upgrade them as tech becomes available.  After I get more logistics I'll typically put small-hull fast transports with the fleet for invasions.  When really good engines show up I might selectively upgrade fleets without transports with top-end engines and weapons as killer fleets. 

I'll often take enemy small fighters, bought for influence in the early game, fly 'em to my mining bases or other people's mining bases, and upgrade them to no-engine heavy-type-specific defense-plus-a-gun fighters called Sit n Pound for defense of those resources; occasionally defense after I smash the enemy base and upgrade some of the fighters to constructors. 

And that's it. 

If I'm going the El Cheapo route like I am in my current game, I use just frigates with not a lot of weaponry in the early game to attack enemy fleets and escort transports.  In the middle of the game I upgrade my veteran frigates to use better weapons and a specific defence type.  In the late game I skip over large hulls and start building huge hulled ships with more firepower than the frigates, but again, not completely filled out.

The idea is to not waste a lot of turns manufacturing ships but instead get some ships out there that have decent firepower when fleeted up and can be replaced without too much trouble.  Plus, by keeping the design cost low, I save on maintenance.  However, when a ship has gained hitpoints from many battles, it makes sense to equip it with more firepower and defences.  So I will have particular designs that I only use for those sorts of upgrades.

On the defence though I tend to park one cruiser with the same armament is my frigate, a couple of integrity grids and decent defences in orbit with some throwaway fighters that can be easily replaced.  The cruisers are costly and take time to build, but they can shut down all but the most determined attacks.

DA:

I put only the very cheapest ship in orbit around each planet, solely to prevent unescorted transports from doing snap invasions.  Its very cheapness will let me replace it in one turn, complicating any invasion attempt.  The true defenders are fleets based at rally points.

In my fleets, I typically have a few offense-only medium hulls and the rest larger hulls with the same offense value as the smaller ones, with the rest of the hull space packed with the best defense.  In later battles, I may also include one "tank" with about half the offensive punch and the rest defense.  The role of the "tank" is to maximize the chance that if a total annihilation occurs, my fleet is the last one standing.

Also, when the enemy has the "first shot" super ability, having one survivor is the way to get at least one salvo in.

Note that in some battles when both sides would be all destroyed,, that one ship will remain with one hitpoint and that ship will be the toughest.  That is the same thing as when one fights the DL ships.  The idea is to have my "tank" be that last ship.  Having the last survivor is often the only way to preserve the planet or mining base the fleet is guarding.

I do not put any defense on the orbital defender, and try to fit it into a "tiny" hull.

When I say "cheap," I'm talking serious low bidder contracts! 

1 strat that serves well - only in the early days - are cargo ships w/1 each best sensors/life support, all the engines that can fit with 1 small weapon. These cats can raise pure heck among enemies - annihilating transports, constructors, colony ships (spore ships), asteroid mine camps and defenseless Starbases. When several are used, your enemy will scream for peace in double quick time

  As I played at more difficult settings (DA metaverse games),  I found more AI transports (and colony ships) have weapons;  and AI constructors with engines and weapons.

I'm not talking about armed transports, I'm talking about a warship or ships destroying the defender, then the AI invading.

Quoting LTjim,

reply 17

Although the AI does indeed sometimes put weapons on a transport, I can never recall an invasion of a planet by armed transports.

Never.

Well, the Yor just did it like 3 times in a series of battles for a planet where our borders collide

Jawohl! All i had the 1st time was a freighter sweetly orbiting awaiting orders to begin a trade route. The Yor Xport moved in for the kill. I re took the planet and purchased a defender type ship (like an attack of 1 rating and zero defense) Then 2 armed Yor xports attacked - one dying with me defender whilst the survivor re took the planet.

I'd never seen anything like and i've been playing DA since it came out. Tough level with max AI setting

They may have - all 3 had armor and shields too - low ratings like 3 and 4