The Tiger Moth I have been in quite a bit had full controls for both.
Depends when you go,you will not need a leather coat if the wx is warm,just some warm layers and a fleece or anaorak type thing.
Quite draughty around the face area,the wind curls around the small screen so you will need a neck scarf.
You will have to use their headset,the one I have used has a throat mike so if you get one of these will not be breathing other peoples germs!

The Moth is slow and does need quite a bit of rudder in turns,but you will enjoy it,we fly around 500-1000feet so you get to enjoy the view.
I'm sure you will get better replies from more experienced bods,about the aircraft and where to get the best deal.
Lister