I mean, at the end of the day I don't really know what the motivations were when selecting those particular professions. But here are a few potential things to bear in mind (focusing specifically on the movie, though it was more of a condensation of the original short stories):

• In terms of Mottel being a "poor tailor," it's worth noting both his youth and the fact that he is presumably poor even for a tailor. He doesn't even have a sewing machine! Jews were actually very commonly producers and sellers of handicrafts in the Pale of Settlement in Russia, something which served many of them in good stead when they emigrated to New York and were able to become involved in its manufacturing businesses. Though Jews in the rural Pale generally were small-time manufacturers (in cities they began to branch out more into larger factories, etc), as early as the 1870s sewing machines were becoming popular in Jewish homes, let alone Jewish businesses. Anatevka, which is shown as more rural than a lot of other contemporary small Jewish settlements, perhaps would have been a bit behind the times, but the idea that a tailor at the turn of the 20th century (when the film is set) doesn't even have a sewing machine is surprising. Quite frankly, from a stereotypical-Jewish-parent perspective, who can be surprised that Tevye doesn't entirely favor a poor tailor who doesn't even have a sewing machine as a spouse for his eldest daughter when she could have a wealthy butcher? And on that note,
• It's obviously also worth noting that Lazar Wolf is much older than both Tzeitel and Mottel, and of course had much more time to earn his money. It's also not quite clear that he is actually wealthy per se- though definitely wealthy relative to Tevye, who is poor as dirt. But then again, in many communities being a butcher could certainly be lucrative (particularly for the unscrupulous)- or even require one to be lucrative to begin with. At this time, the Russian government had essentially taken over an old Jewish tax called the korobka, or "box tax." Before the 19th century, it had been imposed by the kahal (or Jewish community) as a way for the kahal to pay for its communal organizations- but with the dissolution of the power of the kahal, the korobka (specifically on kosher meat production) was reimposed by the Russian government itself. The right to collect the korobka was bought by the highest bidder because it was extremely lucrative in the right (or, really, wrong) person's hands- the holder of the korobka also had power over kosher slaughterers, or shochtim, basically giving them a monopoly on kosher meat production and the ability to raise prices at will. Even if the butcher wasn't himself the korobka holder, he still had the ability, particularly if unscrupulous, to raise prices high, and in fact kosher meat was quite expensive in the shtetl with beef in particular generally being out of reach of the poor. And even without this price fixing, kosher meat, which is subject to extremely strict religious laws through which one blemish in a cow can cause the entire animal to be unfit for kosher consumption, is an expensive and tricky enterprise, leading even more honest butchers with the need to charge a bit more to protect against the potential losses in the case of a non-kosher animal. So even if Lazar Wolf was a perfectly honest man who didn't milk his fellow townspeople dry with the korobka, the margins which the kosher meat industry could charge for something that was essentially a luxury product were potentially considerable.