A hair salon is also the safest place you can get your hair done. I know those home box sets are supposed to be mostly safe, but some of them are very cheap, or sourced overseas and can contain very harsh chemicals, particularly ones that use bleach.
Plus, no one ever does the spot test, which you should do every single time.
My aunt once tried one of those home kits and managed to burn her scalp, and now she won't do anything with her hair in case it happens again.
You never know when they might have changed an ingredient, or when your skin might have changed and might have an allergic reaction, so be very careful when doing this at home. In the long run, you won't be saving money if you hurt yourself.