Hey Ashesix, welcome to the forums!
I remember trying to be vegetarian while living with my parents, they were very closed minded. However, through making delicious foods that they liked minus the meat (and dairy in your case) they began to come around. I would start with making very simple dishes that you can make a little more of than for just yourself and offer it to them as an appetizer, that way they can eat their meat in their main course.
I would suggest you start with some dips, like hummus or my favorite baba ganoush. And maybe some soups. these are traditional meals that dont usually have much if any animal product int hem, so they won't be too much of a stretch for your parents to get into.
My parents also loved their tea and coffee, one of the first things I got them onto was nut milk, so take some of those home and see if they like it.
What do your parents eat on a regular bases? I may be able to suggest specific meals I have made that would impress.
My personal favorite vegan resource is Minimalist Baker. The quality of her recipes are VERY high, just start with the simple ones and you can go wrong.