So what we know and can reasonably infer from EP1
Ray Velcoro
Divorced. Alcohol and drug abuser. He has been raising a child that we are to suspect is the product of his ex-wife's raping. We don't know for sure because they had been trying, and they never got a paternity test. Velcoro seems to be a terrible father that genuinely loves the kid. At one time, Velcoro was probably a stand up cop. He took information from a local crime boss named Frank Semyon that helped him locate the man who raped his ex-wife. Now he's a local city detective and he's also on Semyon's payroll. Violence seems to come to him easily. Sweet mustache.
Ani Bezzerides
County detective with a crazy sister, weird guru father, and mother who killed herself. She seems like she's cold with men. Based on the wooden training dummy, the knives on her walls, the books on knife fighting, and the fact that she stored like 3 hidden knives on her body after the shower (belt buckle knife?!?) we can tell that this is a dangerous lady. She seems like the textbook "by-the-book" cop drama trope.
Paul Woodrugh
Former soldier and current state police. Covered in a scar that looks like road rash from a time "before the desert", which makes sense considering he's got a motorcycle problem. Clearly dealing with some kind of PTSD that's left him with some "performance" issues. Suicidal. In a scene with his commanding officer, he mentioned that he was being railroaded because of "Black Mountain" which has yet to be defined. Based on his comments that they were "doing it for America over there" or something to that effect, I'm betting Black Mountain is supposed to be the infamous military contractor Blackwater, which gained notoriety in 2004-2007 for some questionable killings in Fallujah and Baghdad. If he's a former "Black Mountain" mercenary, he's also a dangerous dude.
Frank Semyon
Former small time hood that now runs a casino outside Los Angelas in the small town of Vinci. Based on his reaction to the article, his treatment of the mayor, and his comments about missing city planner Casper, he's involved at the highest levels of city politics in corruption. He currently trying to run a scheme with Vinci city officials to defraud the government of 100s of millions of dollars through construction contracts for the proposed California High Speed Rail (remember the gasps among the illuminati in the room when he said that the government had guaranteed "overages"). Think Tony Soprano and the condominium construction contracts. Apparently, he needs
The Opulent Russian to invest. When someone killed Casper, they took a bunch of Semyon's (bribery?) money.
The Drama
Semyon wants Velcoro to find the person who killed Casper so that he can get his money back. Unfortunately, he has to work the murder with a damaged and suicidal Woodrugh, and a dangerous and by-the-book Bezzerides.