Tales of Adventure MSQ and Job Level which one to do first?

[Stepjam]

You'd need to do both if you instantly want to be at Shadowbringers, order wouldn't really matter.

If you care at all about plot though, I'd highly recommend not doing either, at least not doing the story skip. Shadowbringers is the culmination of multiple plot threads introduced over the course of the entire story. Though getting the point of the story isn't that hard, a lot of it will be more impactful if you are familiar with the characters and what they've gone through up to this point.

[Sebille]

I suppose one could level a job and then try to go through the MSQ. How long would that take?

[Iscah]

I suppose one could level a job and then try to go through the MSQ. How long would that take?

You level a job *by* going through the MSQ, basically. (Possibly two jobs if you're getting overlevelled and want to juggle the two.)

Quests give EXP and are designed to guide you through the game.

Time-wise... this post says eight days if you rush it, though I'd suggest at least a month or two.