On mint.com, when I am reviewing my spending reports, my automated credit card payments (set to pay the whole balance) are showing as "Business Services". Since I already have all of the transactions running through that credit card categorized properly, what is the proper method to remove these payments? I see there is a category called "Hide from budgets and trends". Should I use this, or will this affect numbers in other ways?
Using the Transfer category is the best place to put these categories, as that accurately reflects what the transaction is. If you have your credit card and bank account linked in Mint, the debit and credit to both accounts will net to $0 in the category.
I would not recommend using "Hide from budget and trends" as sometimes multiple (erroneous) transactions pop up and having a category that should but, in error, does not net to $0 will raise your attention to possibly duplicate transactions.
You can ask Mint to always categorize certain transactions in certain ways. On any of your payments, if you click "Edit Details" and then select the Transfer category, you can ask Mint to always make that classification: