not a teacher
I presume that you are not giving them a gift, but are simply handing something to them.
I wonder why you don't want to use "Here you are", which is suitable for most situations.
To just say "Take" is not appropriate. You could say "Take this" in some cases, although it's often an instruction/command.
Where I live, "Here you go" is also commonly used when you are handing something to someone. This might have regional differences.
Student or Learner