Frost mora or opinel.
Lightweights and OD shirt from any surplus.
Water bottle (can be an old 1 litre pop bottle with masking tape on it to protect it)
Small Esbit Stove (I know that they are not liked but they are handy and small, light and reliable).
Mess tins.
Small cheap torch on a lanyard (if you can afford it get a little LED they will save you a fortune on batteries)
Poncho, ex military (good points of this peice of kit have already been mentioned)
A Pack (the swedish army 35l would be as good an investment as any).
Tobacco tin from a friendly smoker or Altoids tin. Inside it have;
Firbeball firesteel and tinder.
Roll matt (closed cell foam, surplus again)
The old issue sleeping bag 58 pattern.
Both the above in black bin liners seperately and another to work as a pack liner.
You could get nearly all of this from surplus stores and it would cost approx £100.
Most people have warm kit and water proof jackets at home, the mess tins could be substituted for a small billy can for cooking over an open fire (if you have permission).
Bivvi bags are generally quite expensive (even ex surplus ones) so a platic bag like the foil packed ones that the RAF get could come in handy.
The only other thing that I would say is a can of Fabsil for treating the poncho every now and then. Socks can be used in layers, just ensure they are in good condition.
Footware is a difficult subject because a lot depends on the type of terrain you will be covering, but if you have a set of sandals they are good for walking around your camp of a night, if not don't worry.
You will find a lot of the kit that you want at home. These are some of the items;
String or cord
Cotton wool (for tinder)
Candles (they won't be long life but they will do)
Housewife (military nickname for needle, thread, safety pins and some buttons) made up from what you have at home or ask your mum if you can have some of hers. Can be kept in a 35mm film container. for equipment clothing repair.
Small first aid kit made up from what you have at home (Paracetomol, plasters, antiseptic wipes) placed in a zip lock bag.
I hope that this is of use