"Have to" is the most standard, grammatically proper phrase: "I have to go to work now." "I have to go now."
But sometimes, in casual conversation, some people say, "I got to" do something. This is not considered very proper and can, at times, make someone sound a tad uneducated. When people speak quickly, "got to" sounds like "gotta." You can speak this way with friends, but I would advise using "have to" most of the time. However, it's fine to text a close friend, "I've gotta go" or "I've gotta go to work now." Just remember not to speak this way in more formal settings, particularly with a professor or boss.