So long as you are traveling on one ticket, 60 minutes is the minimum time which UA permits for a connection from domestic to international at IAH. Your bags will be checked through, there will be no additional security, and the US does not have any exit formalities. In addition, if your inbound flight to IAH is late and you miss your outbound, UA will rebook you. Nonetheless, if this is stressful in any way and you are not in a hurry, why not book the 3-hour connection. It will take you 15 minutes to offload from your first flight and UA will start boarding your second flight 45 minutes before scheduled departure. That leaves only 2 hours to kill and gives you plenty of time for a sandwich and coffee.

If you travel on separate tickets, then it is up to you. You take all the risk and I do not advise it. If you must do separate tickets, definitely allow the three hours.