The first thing you should do, regardless of where you've decided to meet, is to check the teacher's photo ID, CRB check, and any other supporting documentation they claim to have. Don't worry, they won't take offence at this; they know to expect this as professionals. It is best to do this as soon as you have met and introduced yourselves, so you can concentrate on what really matters: learning with confidence!
We always recommend learning in a quiet room if possible so that teacher and learner can work without disturbance. Please note that if the learner is under 18 a parent or guardian should be present during lessons. If you have arranged to go to the teacher's home, please think safety first and ensure that you do not visit alone until comfortable with the teacher.
It is helpful to consider exactly what you want to achieve from your language lessons, and to explain this to the teacher. The teacher may want to talk through your motivation for learning a language, and may do some exercises with you to ascertain your skill level so far - don't be bashful, you're not supposed to be able to speak the language yet!
Ultimately, the first lesson is an opportunity to gauge your rapport with the teacher, and their teaching style. Don't be afraid to ask your teacher to raise or ease the pace or difficulty of lessons; equally, if you would like to change anything about the lessons (direction, structure, etc) just mention it to your teacher.