Seneca is the Stoic most willing to admit he is not yet a Stoic. The Letters on Ethics are addressed to his younger friend Lucilius and written, by Seneca's own framing, by someone who has not finished his own training and is sending the news of his progress and his failures. The honesty is part of what makes him approachable — and part of what makes him controversial.
He was born around 4 BCE in Cordoba (then Roman Hispania), trained in Rome, exiled to Corsica under Claudius, recalled to tutor the young Nero, and served for years as the de facto prime minister of one of history's worst emperors. He grew vastly wealthy. He wrote tragedies that influenced Shakespeare. He was eventually forced to commit suicide by Nero in 65 CE on the (probably false) charge of conspiracy. He died, according to Tacitus's account, with deliberate composure, dictating to scribes as his veins bled out.
The contradiction between Seneca's Stoic teaching and his political life is real, and he discusses it openly. He defends his wealth on the grounds that money is a preferred indifferent — useful as an instrument, dangerous as an attachment, and proven not to be the source of his happiness by his willingness to lose it. (He was made to prove this in the end.) The defense is genuine but does not fully answer the charge.
What Seneca brings to the codex is voice. The Letters are not a system; they are the 124 surviving letters (of an originally longer collection — Aulus Gellius cites a letter from Book 22) addressed to a specific person on specific occasions — a friend's grief, the death of a slave, a noisy neighbour, a rough sea voyage, a feast during Saturnalia. They read like wisdom literature in the best sense — particular, conversational, often funny, returning to the same handful of themes with patient variation. De Brevitate Vitae (On the Shortness of Life) and De Ira are the other essential entry points. The Consolations contain some of the most useful Stoic material ever written on grief.
He is the Stoic most often used as a gateway because he sounds the most like a person you might know. The risk, and the gift, is the same: it is hard to read him without feeling that he is talking to you specifically.