In a way, this is an unfair question to ask about Tom because the symbolism, set juxtapositions, and Tom's characterization (especially his guilty conscience, "he thought: Hot, no--guilty conscience.") show that there are two things that Tom values equally. These two are Clare, his "slender, very pretty" wife, and his ambition: "it was not actually true that he had to work tonight, though he very much wanted to. This was his own project ...."
Yet, we do see that the thought of "abandoning" his "creased yellow sheet" drives him to an unreasoned act that very nearly takes his life from him. So in this sense, it is fair to ask, "What seems most important to Tom when the story opens?" Rewording it just a little leaves room to think that Tom's overzealous ambition is just a temporary aberration (i.e., departure from the norm) that he will overcome.
If we start with the strongest textual evidence that Tom allowed Clare to go out the door without him for a movie and that he then crawled out the stubborn, puttyless window for a sheet of yellow paper, then the answer seems clear that, at the moment of the story, Tom thinks the most important thing to him is his ambition, which is symbolized by the creased yellow paper.
If we take the second strongest textual evidence that Tom's thoughts were on his ambition and carefully constructed plans for advancement before yielding to the impulse to go "out there in the darkness, after the yellow sheet," then the answer seems confirmed that, at the moment of the story, Tom thinks the most important thing to him is his ambition. Here lies the internal conflict of the story.
It must be noted that after seeing Loew's theater--the implied location of Clare and the movie--and after reaching the window in comparative safety (he did not fall any of the times he nearly fell), his viewpoint is radically altered because when he punches in the window his one word is "Clare!"
[With] his nerves tautening [he] thought of Clare--just a wordless, yearning thought--and then drew his arm back just a bit more, fist so tight his fingers pained him, and knowing he was going to do it. Then with full power, with every last scrap of strength he could bring to bear, he shot his arm forward toward the glass, and he said, "Clare!"