Don't worry about a trophy for your first hunt. Go have a good time and learn about the animal. When you kill one, make sure that you butcher it and put it straight into a cooler. Do not ride it around in the truck all day. That is the biggest mistake people make with antelope. Get them taken care of and you will have some excellent eating. Do not take it to a commercial processor, as you may end up with someone else's mess.
The .243 is a great rifle for your hunt. Use 85+ grain bullets (I prefer the heavier 100 grain Hornady Interlocks in my 6mm) and shoot for the lungs. They are not hard animals to kill and their lungs are big.