From my home gym in Fairford.
I have various equipment including:
Squat rack
Running machine
Air bike
Punch bag
Battle Ropes
Kettlebells
Dumbbells
You don't need any at all as I can help you from the very beginning of your fitness journey.
Depending on your goal I would suggest one or two PT sessions per week, you should also try to exercise another couple of times each week but we can discuss this when you come along to the sessions, and incorporate it into your plan.