Stellaris Fleet Suggestion

I have a general fleet guideline that I stick to as I unlock technology and resources to support it, eventually having multiples of the fleet that you can merge together or split apart as need be. It breaks down as a 1>1>2>5 ratio of battleship, cruiser, destroyer, corvette.

Corvettes come first, and I keep two types, one with two plasma casters and a torpedo, and one with two plasma casters and a point defense. Early in the game, this is the backbone of my fleet, with the other ship classes being support, while late in the game they work as a cheap screen for absorbing tachyon lances. Depending on your FTL method and thrusters, you can generally get away with three shield and two generators, but if you don't have enough power, go with two generators and three crystal hulls.

Destroyers I use as a weapons platform for tachyon lances. The other people who mentioned that they're the best weapon in the game are 100% right, and I try to get them as early as I can. I generally will have two small torpedoes on the other half of the destroyer, to add to the missile swarm and encourage them not to rush in and die. These won't have enough power to run any shields, so go with crystal hulls as soon as you can.

Cruisers work as the large-scale point defense that becomes necessary mid and late game. I use the hangar section, the front end with one medium weapon, and all small slots. Every small slot gets PD, the hangars get fighters (which are the best possible point defense, and pretty good offensively to boot), and the medium slot gets a plasma caster, to encourage the Cruiser to keep to the front of the formation and be useful and stuff. Cruisers are big enough that you can choose between crystal hulls or one capacitor and shields. I generally prefer recharging shields, because it means that there's less repairing that needs to be done after engagements, but if you're playing multiplayer where everybody uses shield penetration, then crystal hulls are the way to go.

Battleships are clearly the coolest ship types, and I have two overall types. The first is all large weapon slots, just stacking as many tachyon lances as possible. I generally go full crystal hull, because tachyon lances take so much energy, but you can still manage to get a decent amount of recharging shields. I also forgo any auras, because of the tachyon lances. The second type of battleship is a supercarrier/aura support ship. One tachyon lance, three hangars, and all other slots are torpedoes (you can mix some extra PD in there if you're facing someone who like torpedoes as much as I do). For the hangars, I use two fighter wings and one bomber wing (or amoebas), to give you an overall 3 to 1 mix of fighter to strike craft. These are also your aura ships. You can have three types of auras active at a time, one offensive, one defensive, and the interdiction aura. I try to run with shield regen and enemy fire rate down, but you can switch them out extremely quickly depending on your enemy.

For a full fleet, I'll run with 4 lance battleships, 6 supercarrier battleships (2 of each aura), 10 Cruisers, 20 Frigates, and 50 Corvettes, split evenly between missile and PD boats. You can order them to determine who engages first by merging and splitting, but I find shuffling them together to work best, since they're all pretty specialized, and will separate based on speed anyways.

The overall strategy behind the fleet composition is to engage at really long range with as many tachyon lances as is feasibly possible, while also overwhelming enemy PD with fighters, bombers, torpedoes, and eventually the corvette swarm. Fighters have excellent survivability against PD, are amazing at PD themselves, and have pretty good DPS if they don't have missiles to contend with. Bombers are simply the highest DPS in the game, and if you've overwhelmed an enemy's PD with your masses of fighters and bombers (you'll have 40 strike craft engaging at the start of the fight), torpedoes are top notch.