Entry By Constructor & Photographer Warbear. Updated 07/31/22

When shopping for new frigates it can be difficult to understand exactly what everything means and what to pay attention to. I will attempt to explain the basics here based on my own research from community sources as well as my own experience buying frigates.
So, what are we looking for when we shop for frigates?
C class frigates with low number of completed expeditions are ideal because that gives them room to level into better S classes.
Not only only is it cheaper to buy C class and level them yourself, you will almost always get a better S class eventually this way than buying one in the wild.
Frigates improve stats only until they hit 55 expeditions completed.
This is why we are looking for ships with low expeditions. If you buy a C class but it has a high number of expeditions already, its likely it will not be able to hit S class before it stops gaining stats at 55 completed expeditions.
Buy with main stat 20 or higher and as low missions completed as possible.
This concept is explained more in the linked cheat sheet, but you can almost always immediately dismiss a ship that doesn’t have at least 20 in it’s main stat (For Combat, Industrial, Trade, and Exploration ships).
Keeping under 10 fuel used is ideal, but not necessary if you don’t mind crafting a bit more fuel for your missions.
Many people suggest never buying a ship with over 10 fuel/250ly but it can be hard to find good ships that also meet this parameter. If you’re ok with gathering a bit more tritium and di-hydrogen for fuel crafting, you can go over 10 here if you need to.
Don’t bother with Support frigates at all.
This will probably be contested by some, but support ships in general are a waste of frigate slots compared to getting a specialized ship.
Frigate Expeditions
You want balanced stats in expeditions if possible.
Think of the 4 stats in missions as a shield you’re building a defense against, the higher the number the less chance you have of a ship being damaged.
You want to send enough frigates so the fleet’s rating is at least one star higher than the expedition’s rating.
You don’t always need to send all 5 ships to achieve a high enough rating, but it can be good to send the max amount anyway for leveling them and getting more stats and 5 stars for more loot.
Having a better class freighter with fleet upgrades can give you a lot of extra stats for expeditions.
The freighter can now give fleet bonuses, so it’s not as hard to achieve the stats necessary through frigates alone.
Use consumables (researched in the anomaly) to boost the fleet mission based on what you’re lacking.
Each mission has 3 slots for adding consumable boosts for that mission such as fuel reduction, time reduction, etc.
Finally, get a leg up using DarklordXelrick’s Cheat Sheet
This well researched document is your handbook for all things frigate and expands much further upon the concepts here. I highly suggest keeping the Recommendations tab open when shopping to get a quick reference for if a ship is worth buying or not.