My personal favorites from the endless products I've tested!
need advice on shampoo - Autoglym Car Shampoo
mitt - Lambswool mitt (Meguiars or Dodo juice)
clay bar - Never used one but I imagine Meguiars sell one which should be pretty good
need something that'll get rid of faint scratches if poss - Really faint scratches can be hidden quite well with Autoglym SRP, or a scratch remover works well, I find Farcela G3 Professional scratch remover the best personally if removing scratches by hand or by machine.
also a decent wax - Autoglym sell a HD wax which is good for beginners, Meguiars also sell a gold class paste wax which is quite good judging by reviews I've seen before for the price. Like most things though the skys the limit and there are some waxes by companies like Dodo juice that are alot of money, but I've never tried these so can't comment on them
should that cover pretty much anything? - A wheel cleaner could be a good idea, Wonder Wheels Hot Wheels for stubborn brake dust etc, Bilberry wheel cleaner for more often use, or just soap and water if you seal your alloys once clean. Also a good wheel brush would be an idea, and a good drying towel to dry the car off (pat it dry, don't rub to avoid swirls/scratches.) A prewash or snowfoam could be used if you have a jetwash to also help clean the car before you touch it, to further minimize any scratches.
budget of about £150 for products. - If your budget is £150, id look at maybe getting a used DA polisher from a member on here or eBay and some compounds (Farcela G3 for example), with some practice you can get your car looking perfect. For the minimum, i'd get two buckets, a lambswool wash mitt, AG car shampoo, and a drying towel. Then to get a better clean i'd look into a wheel cleaner and brushes depending on the state of your wheels, and then SRP to hide small scratches, and a cutting polish like Farcela G3 to remove small scratches. Then for the ultimate, i'd look at a DA polisher.
thanks in advance.