Renato Lins  ,
If you use subdivision the quadrangle is the norm.
You can mix quad, triangle and Ngon if you don't arrive to solve the problem and in some case it will be nice and in the other you've got artefacts.
You can use triangle for game and for low poly style  ;)
I am only an amateur and maybe someone will answer you in a more complete way 
for the top of sphere if you have artefact with triangle, by doing a research on topology you can find many differents solution:

I didn't pay attention that it was digging with a cylinder...
It doesn't change anything !
A Boolean operation produces a lot of parasitic points, don'tt forget to check and weld points if necessary.
I made a diagram for you, it's simpler, if your topology/geography of your object is clean, it will be more simpler to bevel and have shaper angle or smooth with some edge loop ;)

 Perhaps, use a sphere (the sphere who cut) with fewer faces and rearrange the Vertex/edges to have a better homogeneous topology.
This will improve rendering with less artifact.
 Jan Egon Preiss  ,
  I'm really happy to have known these moments and to see the evolution.
I forgot to specify, I do this as an amateur, I have other big passions like music and photography and a job with a family too, so not much time.
But little by little the bird is making its nest  ;)