Removing Shoots and Suckers from trees

Dear All,

I was just wondering if I'm doing things right, My trees regularly have branches shooting from the roots or the base of the tree. I usually remove them when ever I see them, I mostly pick them off with my hands but if the shoots have hardened I will cut with a pruning shear.
I'm I doing things right?

That's what I did when I had trees on my plot (moved now and no room for trees here  )

Thanks Mumofstig, Its good to know I may be doing the right thing.