No need to pay loads for a stainless steel bucket - food-grade (white) plastic will be fine for household use. Get one with a lid very helpful if you don't want to have to sprint from the goathouse to your kitchen with a full bucket when it's bucketing it down...
Also I just use a conical shaped filter/fine sieve and fold a large filterpaper to fit - I buy from Goatnutrition.co.uk.
I am a bit fanatical about teat-dipping (it has reduced my problems with Mastitis significantly) - so a teat-dip cup and I make up a weak solution using Capriclense. All available from Goatnutrition.
Teat wipes from Teisen, through my usual feed merchant.
Uddermint is good if udder a bit lumpy, just don't wipe your eyes until after you have washed them... For general use I use "Botanica Natural Herbal Cream", not cheap but smells lovely. Normally only needed in early stages of lactaton when udder is a bit full, and often skin is a bit dry.