Taking missions from the same agent

I started playing EVE a week ago, in the process of learning the game.

I passed 5 storyline missions on the very beginning, couple of other missions, and noticed that some agents stops giving you missions at some point.

Will one specific agent stop giving you missions at any time?

Does it make sense to stay with one agent and keep executing his missions?

I believe at some point I should start looking into higher level agents (bigger risk so rewards), but does it make sense to jump between different agents?

Thanks.