Well, a guitar teacher should be able to give you a good idea on what you should be focusing on and how to do it, shouldn’t they? That’s what you’re paying them for after all, and it should be pretty focused given that they will be able to see and hear you play.
But if they’re really leaving it up to you then I would choose technique. Theory you can learn online at your own pace, and improv is something you can practice on your own. Therefore, I think having an experienced player there to teach and critique your technique face-to-face would be far more worth the fee.
+1 on the technique focus. Maybe approach this in phases: establish a baseline of technique over the course of a few months and then pivot to something else (maybe songwriting/composition if your teacher has experience doing that)?
Song writing is a whole other skill so don’t be disappointed if your music teacher can’t help you with that.
Justin’s Practical Music Theory would cover any theory you will ever need.
As for what the teacher can teach you will depend on what skills the teacher has. Do they have a teaching degree from a credible music school or are they self taught.
What did you talk about in the trial class?
I would go for what I do with my students: checking the foundations and fortify where needed
The 6 fields Justin says you should practice are:
For the students I coach that translates more into
good strumming techique and chord grips
Some basic knowledge on how a chord is formed
Work on some songs with focus on 1 particular to train something in there that needs work (F chords; barre transitions, solid up-down strums etc.)
Usually there isn’t too much ear training in the form ob transcribing but I incorporate it on that level by making them record themselves and working with that. They learn from hearing themselves when not playing because then they can allocate 100% brainpower to listening.
Make sure you check your strumming technique and fluent style with your teacher; it is a foundation often neglected. The more fluent your strumming is, the less brainpower it needs and that can be used for other things like chord changes, singing, remembering lyrics etc