Economic growth tends to foster more economic growth

Economies are like feedback loops going into a microphone. (I'm not a real economist, so this analogy will be a little strained. Bear with me.) As an economy heats up, it feeds back into itself, making itself heat up more. The people who are doing well have more resources to spend, and that tends to bring others into the web of activity.

(The reverse is also true: economic woe tends to sow more more woe.)

The ROI on training a mage is immense

You haven't outlined what kind of powers the mages have, or whether they can develop new techniques via research, or how any of it works. But in general, the value that the average peasant's work will generate before they become a mage is so much less than the value they will be able to generate afterwards, that it will easily dwarf the cost of training all but the most useless of them.

Profligate mage training kingdoms will outperform stingy ones

The more mages you have, the more new mages they can train. The more mages there are, the more leeway you have to do far-off deep research, the kind that only pays off when, after decades of failure, you finally figure out how to (oh let's say) heal a previously-untreatable disease, cause an earthquake, or set up a telecommunications network.

Paying for this training won't be as much of a problem as you may think. One of the natural side effects of having a huge supply of mages will be a huge stream of income as people hire them for all kinds of things.

Consequently countries that have very liberal mage training policies will tend to be richer and more powerful than those that don't.

To actually answer the question

Unless the discovery of magic is recent, the world will have probably already progressed into an age of sufficiently-advanced magic to be indistinguishable from technology. Armies will be full of mages doing all kinds of magecraft, and the only use for a non-mage will be as support staff, perhaps bodyguards, and probably also spying.

Economic growth tends to foster more economic growth

Economies are like feedback loops going into a microphone. (I'm not a real economist, so this analogy will be a little strained. Bear with me.) As an economy heats up, it feeds back into itself, making itself heat up more. The people who are doing well have more resources to spend, and that tends to bring others into the web of activity.

(The reverse is also true: economic woe tends to sow more woe.)

The ROI on training a mage is immense

You haven't outlined what kind of powers the mages have, or whether they can develop new techniques via research, or how any of it works. But in general, the value that the average peasant's work will generate before they become a mage is so much less than the value they will be able to generate afterwards, that it will easily dwarf the cost of training all but the most useless of them.

Profligate mage training kingdoms will outperform stingy ones

The more mages you have, the more new mages they can train. The more mages there are, the more leeway you have to do far-off deep research, the kind that only pays off when, after decades of failure, you finally figure out how to (oh let's say) heal a previously-untreatable disease, cause an earthquake, or set up a telecommunications network.

Paying for this training won't be as much of a problem as you may think. One of the natural side effects of having a huge supply of mages will be a huge stream of income as people hire them for all kinds of things.

Consequently countries that have very liberal mage training policies will tend to be richer and more powerful than those that don't.

To actually answer the question

Unless the discovery of magic is recent, the world will have probably already progressed into an age of sufficiently-advanced magic to be indistinguishable from technology. Armies will be full of mages doing all kinds of magecraft, and the only use for a non-mage will be as support staff, perhaps bodyguards, and probably also spying.