Line6 HD 300 or 500, which is very popular recently. For interface, you can buy Line6 UX1 or UX2 which come with POD Farm which provide you a lot effect and simulated amp tones. Also you can use it with guitar rig, amplitube etc.
Why your parents want to interfere with your LG's career decision? Should they be in the way? Why bother to persuade them? Are you still Mommy's little girl? Grow up.