After much trial and error, I've found that I tend to use pretty similar (military) ship class templates from game to game. I'll share mine and I'm curious what sorts of things other people like to use?
First off are frigates. My frigates are usually around 5 kton displacement, with at least 10b km range, and are reasonably fast for their tech level (i.e. 7k km/sec at ion drive tech). They are usually beam combatants, armed with a single 'heavy' beam weapon (laser/carronade/particle beam) and a few point defense railguns. They are primarily used as escorts and are armed to prioritize point defense over ship to ship combat. I usually design a jump variant which drops it's heavy beam weapon and a couple of railguns for it's jump drive. I organize them into squadrons of 4-5 ships. The squadrons can operate somewhat independently and are good for scouting, raiding, and guarding outlying colonies. They aren't expected to be any use against a large enemy fleet, but they can buy time for my bigger ship's to get on station and help out. Frigates don't get shields but do get 4+ layers of armor.
Next up are destroyers. I usually build both missile and beam destroyers and they are usually 2-3 times the size of my frigates. Missile destroyers have similar range and speed as frigates and provide long distance fire support for my beam ships. Beam destroyers have a balanced mix of PD and heavy beam weapons and are faster than my frigates. Beam destroyers are better at killing enemy ships than my frigates are due to their heavier weapons, but sometimes will need support from other ships for PD if the enemy is spamming missiles. Destroyers get better armor than frigates, usually 5+ layers and may also get shields if adequate shield tech is available. Jump variants swap weapons for a jump drive similar to cruisers. Destroyers operate in squadrons of 4-5 and usually operate with cruisers and frigates as support ships, capable of chasing down targets of opportunity with their high speed.
Next up are cruisers. I build usually two types, beam cruisers and strike cruisers. Beam cruisers are basically scaled up frigates. They travel at the same speed as frigates and have similar range but have armament that is balanced more similarly to destroyers. They usually gets shields and 5+ layers of armor. Whereas destroyers can occasionally be overwhelmed by missile spam, cruisers are big enough (usually 25 kton displacement) that they can carry enough PD to hold their own. Strike cruisers swap armament for hangar bays and carry marines for boarding enemy ships and attacking small outposts. Jump cruisers swap armament for jump drives. Cruisers operate in squadrons of 4-5 and unlike smaller ships they are capable of operating without support in many cases.
Next up are battleships. These are usually twice the size of cruisers, are heavily armed and armored (6+ armor layers) and always get shields. Similar to beam cruisers they carry both PD and heavy beam weapons and have similar range/speed as cruisers. If available, battleships usually have the heaviest beam weapons available (spinal laser/particle lance), which gives them better alpha strike than cruisers but generally lower DPS. Jump battleships trade weapons for jump drives similar to other jump ships. Battle barges are similar to battle ships but trade weapons hangar bays filled with marine strike craft. Battle ships are generally capable body operating independently but I usually group them with other ships. Usually I will augment my cruiser squadrons by swapping out a cruiser for a battleship, but occasionally I will group battle ships into their own squadrons of 4-5 ships (especially for jump point assaults where the smaller cruiser jump drives can't squad jump a battleship).
Finally, carriers. I only build big carriers, same size as my battle ships. They use commercial engines and are very slow, but they get much longer deployment times than my other fleet ships and usually hang out way behind the front lines with the rest of my support ships where they can't be seen by potential enemies. They are almost always filled with missile bombers and carry large enough magazines for a few reloads. They are usually used as a strategic asset, capable of providing a huge amount of alpha strike capability when my beam ships are struggling against higher tech or more numerous foes.
I also occasionally build smaller ships, like 2500 ton corvettes. These get a PD weapon or two and a heavier beam weapon and are designed to be as fast as my fire controls will track. They have very short range and mostly hang out in orbit of colonies to chase off nosy survey ships or other interlopers.
That's about it for my 'standard' ships. Feel free to comment or share your own.