A short note: This is probably one of the most difficult cases to compose a profile for. This is so for two reasons. The first is that we have no knowledge of the fourteen murders committed before the beginning of the episode. The only ones we have to consider are Deputy Scott Kerber, Agent Frank Burst, Agent Collins, and the guard and the technician at the hospital. The second reason is that none of the crimes were really committed by Modell. There's no physical evidence to base a profile on. What's left is victimology and psychology. This isn't what a profile would usually look like.
Modell, as was classified by Mulder and Scully, is a highly intelligent sociopath. More specifically he is an Aggressive Sociopath - he harms others for gratification and assurance of his power. This would explain the course Modell chose to take with his new ability, once he achieved it. Aggressive Sociopaths often seek out positions of power and authority for the same feeling. Modell served in the army, and applied to the FBI. Being rejected from a the Bureau most likely intensified his dislike of authority.
Age: While it is hard to be deriving an age from the case itself, we have noticed that Modell is in his thirties. Without this insightful bit of information the viewers have, an estimate may be made of 32-37, since the killer is experienced at what he does.
Intelligence: As is observable, as well as derivable from the case, Modell is extremely intelligent. He's managed to not only get away with the fourteen murders he's committed between April 1994 and the beginning of the episode, but managed to evade arrests more than once throughout the episode. He's aware of how intelligent he is, which is why he finds it so frusturating to have washed out of both the Navy Seals and the Army Green Berrets.
Education: Despite his high intelligence, Modell attended an average community collage. This is explained by a lack of ambition which is characteristic to sociopaths. (This also explains his last known employment which was, according to Scully, a convenience store clerk.) However, he demonstrated a fairly thurough knowledge of diseases, since he was able to pick one that would suit Agent Burst and expand on it fairly quickly. This means he either has an interest in medicine and has either read books on the subject or has taken some medicine-related classes during his time in collage, or he prepared especially for Agent Burst.
Family: Since most sociopaths come from fatherless homes, it can be assumed that Modeel comes from such a home as well. This is confirmed in "Kitsunegari" - he has spent most of his childhood in foster homes. From the events of "Pusher", Modell behaves like someone who is alone in the world and has no one but himself to worry about, which is what he does. However, in "Kitsunegari", he behaves like an older sibling, protecting his sister as much as he can and trying to stop Mulder from playing her game since it would hurt her in the end.
Residence: Modell's apartment is relatively small. He keeps in it only things that he needs (his medication, his protein drinks) and things that he finds useful (his books, television). The lack of decoration isn't for a lack of money (a contract killer makes a good dollar) but for a lack of caring. There's no information in the episodes about the location of the first fourteen murders, but they're most likely far from home, since he tends to keep everything from his his grocery shopping to his cancer treatment far from home.
Vehicle: We've seen it. It's ugly. Modell drives an old car, probably the same one he's had since April 1994. However, it's kept in good condition and it's clean.
Employment: This is an area where there's a little more to base on. While Modell did apply for the FBI, the Green Berets, and the Navy Seals, he ended up serving as a supply clerk in Fort Bragg. He got nowhere in life because it was his intention - Sociopaths have no life plan. His last known job before becoming a killer for hire was a convenienve store clerk. This was most likely the last in a series of dead-end jobs.
A Little About Modell's Psyche: Anyone who's seen "Pusher" can tell you what Modell's MO is - "Haven't you caught on yet, Mulder? They all kill themselves." This, as Mulder stated, makes for the perfect MO. It in no way leads back to Modell. This modus operandi can also tell us a little about him. A sociopath's conscience is distorted, so by convincing himself that his victims all kill themselves, he can walk away with no feelings of guilt and perhaps even with the feeling that he's done the world a favor.
He most likely sees in his home a safe haven. Nothing is allowed to come close to it. One of the payphones in his magazine ad is in Falls Church - almost 9 miles from his apartment. His oncologist is in Fairfax, 14 miles away. He does his grocery shopping in Loudon county. That's 20 miles away! Actually, the closest he was to home in the episode is the FBI building in Washington DC. His "safe zone" is probably about 5 miles from home.
He studies martial arts as well as eastern philosophies, such as Tai Chi and Budo. While he believes that the techniques enhance his mind-control ability, he does not fully believe in them. He doesn't disregard his own death. Quite the opposite, he values his own life over anything. His game of russian roulette with Mulder was just another thrill for him, one that he was convinced he was going to win. Adding Scully to the circle was a last minute decision. Killing her wouldn't do him any good. It's Mulder he's after, not her. But adding her in increases his chance of living through.
Modell's cat and mouse game with the FBI may have had more to do with the thrill and the risktaking than his medical condition. His words while arrested in the beginning were, "You think you can hold me?" He has no intention of being caught, only of seeking the thrill of the chase. Also, his search of a "worthy opponent" shows that he doesn't care about how long it'll take him. He's willing to wait as long as it'll take until he finds someone worthy to face him. If Mulder hadn't come along it's not likely that he would've just said, "Hey, Agent Burst, wanna go one on one?" and left it there. It's not enough of a victory to him.