In both examples the -ing form is correct.

"I always read before to go to bed" is just wrong. "to go" what is to go? You could offer "I always read before I go to bed" His problem, to find a new job, was his lack of experience. This needs punctuation to make it work as shown.

This is a good question and the two forms say the same thing, yes. I think foreigners who learn English much prefer the 'ing' form as it is taught to them as being better. Perhaps it is seen as something exotic and particularly English? Who knows. Anyway, in practice I think the simpler style is to use the infinitive.

infinitive* :)