My first was on the UP's City of Los Angeles in 1959, a one-way trip when my family moved from suburban Detroit (Birmingham) to Costa Mesa, CA. Though I don't remember the trip. I do have the family photo/slide collection, which includes it.
Two years later, we moved back to Michigan (Bloomfield Hills this time), and a couple years after that, we took the City of Los Angeles again--this time a round trip, as far as Las Vegas, where we rented a car and drove down to Sun City AZ, where my grandparents (Dad's folks) had just retired to. That trip I remember--it was fun!
During the '60s, we'd sometimes take the Grand Trunk from Birmingham to visit my other Grandma (Mom's mom), who lived & taught school in South Bend. That was how she;d travel when she'd come visit us.
Unfortunately, my next LD trip wasn't until 1998, when--after moving to northern California, I took the EB and CZ home--with a one-night layover in Chicago--from where my folks lived in Red Wing, MN to Martinez, CA (closest stop to where I lived then).
I made that EB-CZ trip a couple times a year while I lived in California...going through the Sierra Nevada in the winter, it seemed like you were inside a snow globe if you were in the SSL during a snowfall!
Since moving to Florida, I've taken the AT a couple times, the most recent one just about a month ago, to a 40th reunion of my old high school football team.