First, I hope you're not on campus housing. If found with a gun, you'll probably get expelled from your apartment, if not from your university.
Look into getting the LTCH first. Without it, you're going to be severely restricted in where you can go with your handgun. Sure, you can go straight from your home to the range, the gunsmith, etc., but that's about it. You cannot stop by MacDonald's on the way to the range. You cannot stop for gas on the way back from the store. If your car breaks down, you might have a problem. I wouldn't take that chance, since carrying a handgun outside of the scope of law is a very serious crime.
I'd consider a long gun -- probably a shotgun if you're interested in home defense. Correct me if I'm wrong, guys, but I believe you can carry a long gun without LTCH. No, I don't suggest walking around with a long gun, but you can avoid movement problems if you end up without an LTCH. Long guns are also more powerful, more accurate, and easier to shoot than handguns.
I looked at Form 4473, because I thought it had a box which implies that you either had to be a citizen or a permanent resident. But all I see is Box 15, a request for alien no. from non-citizens. So it doesn't seem that the federal government has a rule about it. I do know that some states allow firearm ownership for citizens only. Indiana is not one of them, but I don't know whether it sells guns to international students or gives them LTCH.
If you do get a gun, make sure to get training. Owning a firearm without proper training is a bad idea. You'll be more of a danger to yourself and your friends.
I just read the form 4473, seems like I could get a firearm since I do have admission number.
I am living in campus BTW, I heard one guy get expelled in my campus because people saw his handgun on the waist.
Thank you for your suggestion, you are right, I don't want to get kicked out of here because I carry a handgun, not very smart.