To indicate a state of beginning:
* -ing: beginning
* -ment: commencement (formal)
To indicate something that begins:
* -er: beginner (a person)
* -ing: beginning (a noun - the act of starting)
To indicate the result of beginning:
* -er: beginner (a person)
* -er: opener (something that opens)
* -er: starter (something that starts)
The best choice depends on the specific meaning you want to convey.