Your English is fine . . .
-Will it be powerful enough? (it doesn’t need to be super fast) Yes
-Which OS should i use? (which Linux? Ubuntu?) Debian
So in this specific context, Ubuntu versus Debian may matter less, but Ubuntu is not exactly a server distro. Like any other flavor of Linux, it can be made to do anything other Linux’s can do but . . . Debian should not let you down.
Just so you know, the BBB is actually rather fast with network transfers via the ethernet interface. That is considering it is 10/100 fast ethernet. You can nearly max the interface speed wise.
I would pick up one of Robert Nelson’s 3.13.x Debian images, and start learning / testing.