PA-28 pilot reported smoke and fumes filled the cockpit after take off. Pilot requested priority handling and made an immediate air turn back and precautionary landing at departure airport.

Narrative

Departing Runway XXL on the ZZZZZ departure; I was climbing through about 900 ft.; and smoke rapidly started filling the cabin. As well as a terrible smell; like burning rubber. I felt like there may have been a loss of power as well-but in retrospect; I'm unsure whether power loss actually occurred. After this; instinct and training took over. I radioed ZZZ Tower; [requested priority handling]; and said that I wanted to land on the Runway behind me. I turned to land on XXL and set up for a left-ish downwind. I had enough energy to either slip it down or perform a power off 180. There was an airliner on the Runway that wasn't able to move out of the way. I didn't want to hit them; so I looked for another spot and saw Runway XYL. There was another airliner on that Runway; but I judged that I had enough space to slip it down; land; and stop without hitting them. So I cut the power; landed on XYL; and cleared the Runway at Taxiway 1. Upon landing; I was in shock; the smell got worse in the cabin; so I shut everything down; grabbed my handheld radio; and exited the aircraft and told ZZZ Tower I was OK and clear of XYL. I am still trying to figure out what happened. I am still at the airport; I was able to find an A&P; and he is helping diagnose. I consulted with an avionics shop and there are no signs of an avionics fire. I'm also still somewhat in shock. And almost questioning my memory of what I saw. I think that more attention to aircraft maintenance; and going above and beyond the basic requirements (e.g.; an annual inspection) that the regulations specify would've helped prevent this. I haven't been happy with the quality of my flying club's maintenance. And I learned that my flying club hasn't asked our A&P to inspect the engine since our last annual. He's just performed oil changes. While this isn't against the regulations; this doesn't meet my personal standard of safety.