The same as in eastern towns for the most part. The most essential jobs were blacksmith, sheriff, lawyer, leather worker (shoes especially), and merchant, with saloon keeper (and sometimes whiskey maker), banker, and postmaster also coming pretty soon to each town, as did printers and sometimes telegraph operators. Prostitutes were of course rampant, sometimes the majority of women in towns, with preachers usually a distant last. Physicians and surgeons usually came earlier, but few had what we would call "formal education"; surgeons were the least skilled (they were men who could set a broken leg or take out an arrow or saw off a limb if needed) while physicians treated illness (flu, cancer, consumption, etc.) and doubled as pharmacists and sometimes as dentists if there wasn't one already. In most small towns (both east and west) surgeons and physicians often treated both humans and horses and other animals, and they also usually treated the STDs of the prostitutes on a weekly basis to control public health. Many of them had gotten their starts as medical professionals in the Civil War, where the same injuries and diseases were the same as the west (gunshot wounds, infections, prostitutes and soldiers with STDs, and various airborne illnesses like measles and other contagious diseases).
Mark Twain described Virginia City, a silver and cattle boom town in the 1860s when he lived there and where he began literary career, this way:
"Money was as plenty as dust; every individual considered himself wealthy, and a melancholy countenance was nowhere to be seen. There were military companies, fire companies, brass bands, banks, hotels, theatres, "hurdy-gurdy houses," wide-open gambling palaces, political pow wows, civic processions, street fights, murders, inquests, riots, a whisky mill every fifteen steps . . . a dozen breweries and half a dozen jails and stationhouses in full operation, and some talk of building a church."
Added: gunsmiths, of course, were a much in demand profession as well. Once again, many of them had their training in the Civil War where guns had to be constantly repaired or improved.
And a surprising much advertised for profession in the Old West was musicians. A good musician/singer could make a fortune in a place where there was no modern type of recorded music or entertainment and most saloons/brothels offered dancing girls.