Bism Illah wa as salaamu alaykum.
To live and work professionally in Saudi Arabia, the best chance of getting work is to aim for the teaching profession or nursing.
I don't have experience about nursing, but I do know that a Bachelors Degree in nursing is the best way to get a decent job. Bear in mind, however, that there are people from many countries that will come here with the same qualifications for lower salaries. Therefore, someone from the USA, UK, or Canada may struggle to find a decent paying position in nursing because qualified nurses from the Philippines, India, and similar countries will come for a much lower salary.
As for the teaching angle, at minimum, a Bachelors Degree in a given subject is needed. One of the biggest areas where jobs are most available is teaching English as a Second Language (ESL). There is such a big demand that not only do the universities hire directly, there are companies that hire teachers and them supply them on contract to the universities as well. To teach ESL at a university as a direct hire, at present, one needs a Bachelors Degree and a TEFL, TESOL, CELTA, or DELTA Certificate with at least one year teaching experience. The more longer the teaching experience you have, the better your pay scale.
To get a position that is more secure and better paid, a Masters Degree and more experience is preferred. However, there is a good chance that the MA will have to be in ESL or Linguistics in the future to ensure you are retained.
Contract companies that hire people and then provide them to different universities and institutions often have lower requirements. They sometimes take people with less than a BA, as long as they have an Associates Degree and good TEFL experience. This is an option well worth exploring.
To teach a different subject in a university, one must have either a Masters or a Doctorate in their subject/field. It is easy to see what qualifications are required for each position as they are listed on the job vacancy notice.
To teach in Madinah, one needs to look at Taibah University. Simply go to the website, click on the job opportunities and see the large variety of jobs available. To teach in Jeddah, go to the King Abdul Aziz University website. Basically search for the university in the area you would like to live, and be flexible because if you get a job in Taif, it is only 45 minutes away from Makkah.
One cannot just come and visit and try to find a job. It is possible to job hunt while on an Umrah trip, but the procedure is such that you will be hired from your country of residence and all visas and travel protocol and procedures must be done from there through the Saudi Embassy. Your employer will be bringing you into the country to work.
Okay, that is the beginning of this subject. I hope to post some other blogs, which are very helpful for people trying to live and work in Saudi Arabia, inshaa'Allah.
Barak Allahu feek!