'to commence' is kind of stilted and not so much in use in spoken English as 'to begin' . They mean the same though!

They do mean the same thing, but commence is more formal.

commenced would be better for your sentence because its more formal. begin its very casual, something you use with friends. I begin to think that I might not get to work in time. The soccer game with begin in 5 minutes. The elections will commence next month. you can pretty much replace them with one another, but commence is very formal. your friends might look at you weird if you use commence around them.