Which would be a better option to settle abroad: go for my masters and live there or start working in my country and relocate?

Student visas are temporary NON-immigration visas issued on the condition that foreign students return to their country of citizenship immediately upon completion or termination of studies. You cannot legally remain in the country where you go to school. Intent to remain when applying for a temporary visa is visa fraud, grounds for visa denial or revocation with deportation (mandatory departure) and permanent bar to entry.

You are going home & get several years of experience before you might find any qualified employer willing to pay the vast amounts of time, money & hassle to apply for your visa. Furthermore, visas are only issued at consulates in your country of citizenship.

Bachelor's degrees are as common as grains of sand on a beach. Nowadays, master's degree holders, especially among those who want to relocate to other countries, are abundant. You typically have to compete with hundreds (even thousands) of applicants from around the world even if you have a good master's degree in a STEM occupation.

Get educated in your own country. It will be far less expensive. Once you have your advanced STEM degrees, start working, and publishing. Then look for sponsorship to immigrate.

Depends if you have the necessary funding to pay for studies or immigration. In Canada, foreigners pay much higher university fees and immigration requires a lump sum to demonstrate your ability to survive.

In most countries, studying there does not make you eligible to stay and work there. It might put you in contact with companies who would then sponsor you for a work visa.

Student visa are non immigrant

you do the course and return home ..its not a back door

to immigration