I have had to make a few assumption to answer your question.
That you are going during the summer months.
That you have a car to carry your luggage.
That you are staying in accomodation and not camping.
You will need a day rucksack, one that holds around 25/30 litres.
Walking boots that are well worn in to save you getting blisters. I suggest 2 or 3 season walking boots in fabric material.
3 pairs of walking socks.
1 pair of lightweight walking trousers.
1 pair of walking shorts incase its hot!
A lightweight waterproof jacket and waterproof overtrousers. (hopefully these will spend all week in your rucksack, but you never know)
3 tee shirts, ones that wick moisture away from your body. Anti-bacterial ones are even better.
A warm top to wear over your tee shirts.
A warm hat.
Enough underwear for the week.
Map or maps of the area your going to.
A small first aid kit.
A useful book of the area.
A small flask
A watch, telephone, small torch, and whistle for emegencies,
Clothes to wear for when your not walking.
Sandals to let your feet breath after walking.
Hope this helps.