Could you please specify more exactly what you're interested in? Antiquity encompasses a period of several thousand years, with myriad peoples and cultures interacting with each other for every moment of that time. Depending on time and place there are vastly different cultural and social attitudes and approaches towards various means of accumulating wealth and various trades. For example, while the mercantile classes appear to have been fairly powerful and prestigious at Carthage, you won't find the same respect for merchants in Rome even as late as the Principate.

In addition to when and where it might be worth it for you to clarify what you mean by a profession and what you mean by "sought-after." The first is mainly for the purposes of semantic (and rather pedantic, sorry) clarity--members of the senatorial class were not ideally supposed to have a profession, as in a trade, and made their money off of land-trading and rents mostly, which we might consider a profession but not an occupation. The latter is essential to your question, however--do you mean professions that are the most respected or those that are sought after because they provide the greatest opportunity for wealth? Those are not necessarily the same thing--to use my Roman example again, while merchants often could amass large fortunes the occupation was dominated in the Principate by non-nobiles and freedmen