The first thing you should do, regardless of where you've decided to meet, is to check the tutor's photo ID, any DBS checks they profess, 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!
We always recommend learning in a quiet environment so that tutor and tutee can work without disturbance. Please note that if the tutee is under 18 a parent or guardian should be present during lessons. If you have arranged to go to the tutor's home, please think safety first and ensure that you do not visit alone.
It is helpful to consider exactly what you want to achieve from your lessons, and to explain this to the tutor. The tutor may want to talk through your motivation for studying the subject in question, 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 be an Einstein yet!
Ultimately, the first lesson is an opportunity to gauge your rapport with the tutor and their teaching style. Don't be afraid to ask your tutor 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 tutor.