To answer your questions more specifically.
Replace gutters before painting.
If you want a new look for your gutters should you paint them or undertake a gutter replacement.
It s constant runoff from your roof that would eventually cause problems.
Before getting started painting your exterior calling a painting contractor or replacing gutters you need to think what color scheme you would like.
If they are due for replacement getting them done before or during the exterior painting process makes sense especially if your painter has the chance to paint the gutter boards once the old gutters are removed and before the new ones are installed.
If your rain guttering systems are working correctly the side of the building should be protected from excessive moisture.
If you get some rain or even a storm before the new gutters go up that s no big deal.
If there is paint peeling on the sides of your house it may be an early sign of water damage.
Avoiding the need to paint.
It s important to clean your gutters seasonally to prevent debris buildup.
If you can prevent your gutters from clogging then you can stop a lot of those gutter problems in the first place and you won t need to worry about gutter painting or gutter replacement.
Before exterior painting or replacing gutters.
Often problems with gutters sagging and getting full of debris begin with gutter clogging.
The reason is simple in that gutters only come in a limited number of colors while paint colors are infinite.
If you are replacing them chances are you are limited to a choice of colours.