He had a Kalashnikov of some sort, a handgun of some sort, and what the New York Times describes as a "22 long rifle." .22LR is the name of a cartridge, not a firearm, and you can fire it from handguns or pistols, so your guess is as good as mine on that one. He's reported to have exchanged hundreds of shots with police. That'd be a little surprising. Ammo is hella expensive these days, and most people don't keep vast amounts of it on hand, though Poplawski was reportedly stockpiling. If I had to bet, I would guess that his first murder, as the police were coming in the door, was committed with the handgun. Subsequent murders probably done with the AK. I do wonder, though, if a lot of the rounds he exchanged with the cops after the murders were .22s. Because it's not uncommon in the slightest to buy hundreds of those at a time.
My guess is that the shootings were probably relatively impulse-driven. Example of previous behavior: Poplawski joined the military. Than he decided he missed his girlfriend and wanted to see her. So he deliberately got a dishonorable discharge. Yeah, that's thinking ahead, guy. While the murders were likely not politically motivated, it turns out that Poplawski is a political fanatic and active white supremacist who believes Jews run the country. He posted regularly to the white supremacist Stormfront forums, and had tattoos related to the movement. Also, he had domestic battery charges from roughing up a girlfriend, and was arrested for violating the order of protection she had against him.
Gun owners reading this will have had two alarm buttons go off: what was this guy doing with firearms? The domestic battery stuff and the dishonorable discharge mean that he is legally prohibited from owning guns. Those are two of the questions on ATF Form 4473. Whatever guns this guy had, he had illegally. Be interesting to know how he acquired 'em. If he made a straw purchase, then the guy who made it for him is going up the river, big-time.