Professional fields can be divided into two groups on the basis of how easily skill is assessed. That difference cascades into many other aspects of the professions and governs much about work life within them. It will determine how important other factors are, like pedigree, fame, and luck.
Where a skill is easily assessed, a person can readily rise through ability alone. The definitive exemplar is computer programming, especially in earlier decades. A college degree is not important; working with a famous mentor is not very important. All that matters is ability, which can be assessed by any other skilled programmer. The meritocracy this creates has become a part of programmer culture, which reinforces it. But as a result, external markers of success are much less relatively important to career success: the ability to network, and self-promote may help a little, especially at the upper end where skills tend to plateau, but are not decisive. This also results in fairly predictable career advancement, at least until management positions are accepted.
At the other end are careers like acting. Skill is important but very difficult to assess -- and heavily subject to taste, preventing any absolute evaluation. In such a field, external markers gain prominence: where one attended school, what mentors one had, who one knows. All of these create fame. Fame feeds into itself, so that famous people attract more attention and more prestigious job offers. The snow-ball of fame does take some time, but can be triggered by very small beginnings. This means fame-dominated careers are also dominated by luck. And because snow-balling fame grows exponentially, not at a constant pace, this creates large disparities in success: a few people make it very big, while most barely make it at all -- in contrast to the steady climbing in programming. This is not to say that a famous actor is not skilled, but that his success is likely out of proportion to his skill, and that many equally-skilled peers have not succeeded as well, purely becausse of poor luck, pedigree, or connections.
Among the skill-dominated fields are many technical careers like engineering, accounting, and nursing. While some training and accreditation may be necessary, these matter little upon entering the work-force: experience and demonstration of skill will gradually earn promotions or at least ensure steady work. On the other end are many fields where radical success is possible, like in politics, entertainment, finance, and management. We can say these are fields where skill is hard to see, and must be inferred from success. But they may be susceptible to bullshit and self-promotion. Less kindly then, one could say skill simply matters less in such spheres.
There is a continuum, of course: fields in the middle may involve a mix of skills, with some easy to assess nad others much less so. Graphic design is one: the basic technical abilities are straight-forwardly shown but creativity or aesthetic sense are not, so marketing and self-promotion are necessary parts of the job. An interesting side-effect develops from such an in-between position.
All fields need a means to exclude outsiders and keep the ranks from swelling too much, driving down wages. In computer programming, becoming (self) educated is fairly difficult and beyond most people -- even though the barrier to attempting it is very low -- so a restriction is built in. Thus, even though the 90s dot-com boom saw many people trying to enter the field for good jobs, not everyone could, so there was no monstrous glut of programmers (until the bust). The film industry meanwhile is regulated by enormous disparities in success: the relative value of fame keeps it in short supply, so the vast majority of want-to-be actors cannot enter the field except at the margins. Only a few will get lucky breaks to become genuinely full-time, working actors.
In many of the intermediate fields, neither of the above mechanisms keep out a glut of interested young people. In graphic design, the basic technical skills are easily assessed but also fairly easily learned. There is some gap in fame, to be sure, but also a demand for a lot of workaday design, far from New York City ad agencies. In an appealing field, what keeps everyone from entering and climbing quickly to middle positions? This is an industry where people "pay their dues": young entrants must expect very low pay for many years, and usually suffer multiple internships -- often without pay at all. This effectively selects only the most driven workers, or those whose parents have money.
Any field with middling assessability of skills, and which is generally appealing (monetarily or otherwise) is likely to require internships and other rights-of-passage that test applicants' motivation and family wealth. Skill will also be considered, but is not sufficient. Academia springs to mind as another prime example: only many years of slow study with great uncertainty and low pay allow entry to the professoriate; networking and fame are important at the upper levels (among researchers) but demonstrable skill is also required.