@thomas_4As an introduction, I'd say you should read five stories in their release order:
01 Average Joes by Thinking Horndog
As others have said, this is the first story and it lays out the universe.
02 Pickup Number Eighteen by Thinking Horndog
The template for pickup stories. Many early stories especially start with a pickup scene.
06 Buying Wholesale by Thinking Horndog
A large scale pickup, but more of the same.
09 Civil Service by Duke of Ramus
An idea for a non-combat branch of the Confederacy.
10 Neptune by Duke of Ramus
More in depth on what the Civil Service does and the problems they face.
These aren't necessarily the best stories, but they introduce a lot of the templates and ideas that are still being played with 300 stories later.
I'm also going to recommend a couple of things. First, pay attention to story codes.
While that's always true, remember that the Swarm Cycle has a lot of bdsm elements baked in to the universe, especially sex slavery. Some of the Swarm stories get really rough. Likewise if a story has tags for incest, violence, rape, and so on. Some tagged stories will be mild, but many go to extremes.
Second, pay attention to word count, longer is not necessarily better. Again, this is true throughout SOL, but there are a lot of stories in the Swarm Cycle that are just endless repetition of the same content: pickup happens, we're introduced to a few characters, they have sex in various combinations, learn about the Confederacy, repeat.
As a frame of reference, a mainstream published novel is usually in the range of 80k - 120k words depending on the genre. So if a story is 250k and the description is one sentence, be conscious of whether the setup is enough to support the equivalent of a trilogy.
Third, there is an official canon and some stories only loosely adhere to it. This doesn't make them bad, but it's something to be aware of. Also, the opposite of this is that there are an awful lot of stories, especially early on, which are pretty much the same except for the names.
In summary, don't feel you need to read everything to understand the universe. Skip or stop reading any story that doesn't fit your needs. It's unlikely you'll miss anything important.