How to clean disk brakes?
In most cases a mild bike wash soap gets you past the minor services, no problem. Used in conjunction with a toothbrush or the like.

What you want to avoid is any cleaner that is oil based(petroleum, paraffin etc.). These leave residue and will affect your stopping power. I have even found citrus de-greasers leaving residue films behind. 

During major services you want to get the wheels and brake pads out after the normal wash. You can then use isopropyl alcohol to bush the caliper out. Isopropyl is also great if you found the pads contaminated and can often save the day from having to buy new ones. In addition, isopropyl is also used to wipe down the rotors' surface and that is very important to keep clean.

Isopropyl alcohol is cheap and easy to find, often branded as some type of household cleaner. So you can add it to the shopping list or swing past a chemist/drug store. In addition, if you are working on brakes, this should be part of your standard tool kit. It is the go-to for removing and cleaning DOT brake fluid of the bike as well. Also, when you go to the auto parts store, they will have brake cleaner as well. Usually more expensive and mainly pressurized isopropyl alcohol.

Avoid sandpaper. This is the very last resort. Unless experienced, you are almost guaranteed to get the surface not flat and out of parallel with the other side and rotor surfaces. This will decrease stopping power, cause squealing and require the pads to be re-bedded. So effectively you'll sand away some of  the pad and the lose more trying to get it bedded again. Have used it in the past for very specific problems and then you'd be looking at 800+ grit, super flat working surface and circle motions.