for the time being there is no use in buying new shampoos etc as you may as well use up what you have already.
If you havent got 2 buckets make sure you have.. if possible have grit guards in them as well.
Get yourself 2 wash mitts, you dont have to spend a fortune on them, a pair of £6-7 lambs wool mitts will be fine. You want 1 for doing the upper body panels and the other for the bottom 1/4 of the sides, the front and rear bumper and the door sills etc.
get yourself a decent waffle weave or mf towel to dry the car with, these are the safest methods of drying your car without inflicting damage
on your budget you arent going to be able to fund the purchase of a machine polisher so your going to have to buy products which mask or fill any light scratches and swirls. AutoGlym SRP (Super Resign Polish) is filler heavy but also contains very light abbrasives, with hand application these wont do a massive amount but it will 
help to hide the marks on the car.
You then need to seal the SRP in so the cheapest and probably best matched product for that is AutoGlym EGP (Extra Gloss Protection). This is applied by hand and left to cure for just over an hour. Whe buffed off you have an ideal finish to lay a wax onto.
There are a few waxes for sub £20 which are very good. Meg's Pro #16 or Collonite 476s are both around the £15 mark and will give a very nice shine and last for up to 4 months. You need to apply 2 layers of wax to ensure total coverage and a decent level of wax onto the car. apply the wax with an applicator pad and get each layer as thinly laid as possible, if you lay too much wax down it wont add to the finish and will just get wasted when you buff the wax off.
For buffing the wax use MF cloths. Buy the deepest pile cloths your budget will allow for removing wax, the softer the better imo.
As your knowledge and experience increases you will without doubt (trust me on this) want to do more and try other products so consider this the start of an obsession !
If you need anymore 
help just ask or check the user guides on DetailingWorld.
Regards, Nige