"I get home" is usually used together with a time; "I get home at 5pm", "I get home 20 minutes after the match ends", "I get home before 7pm most nights" and so on. It's equivalent to "torno a casa"; there's no real difference in meaning between the two. "I come back at home" is not grammatically correct. However you can say "I come home" in some cases. It functions more or less the same as "vengo a casa"; if you can use that expression in an Italian sentence it will usually translate well enough to English.

"I get home" is the most common way to use the phrase.