The second part if the sentence, "for my choosing this major" is perfectly fine and means the exact sane thing as "for me choosing this major." The first way turns the phrase into a noun referring to the speakers choice of major. It's probably used more in academic writing than spoken English. The second way is more common in everyday speech. The first part if the sentence though, while not technically incorrect, sounds a bit awkward. A better way would be to say "there are three main reasons...."

Actually, the most common version would be "there are three main reasons for my choosing this major". "main" should be an adjective modifying "reasons". The version you wrote with an adverb is acceptable but a bit convoluted. We would use "mainly" in sentences like "he was mainly angry, but also a little sad" or "she mainly ran, but occasionally walked".