Trains run all day, you can pick the best times that work for you. There is parking at Wilmington station. Train ticket cost vary depending on the time of day, and the type trains you choose. Early morning trains are inexpensive. I made a reservation coming back from NY but I just showed up at the Wilmington station and purchased a ticket at box office to New York without a reservation.. Again the trains run all day so you'll get on a train even if you have to wait 30min or less. Strictly up to how you like to travel and the budget you are comfortable spending. You can go on Amtrak website and look at schedule to better plan your trip or they were very friendly and helpful at the train station. I can't tell you if there is a charge for parking at the station because I Uber but I did see the parking lot with passengers coming and going.
Look at amtrak.com
Trains Wilmington to New York are available approximately every 30 minutes throughout the day (5a - 1130p). Fares vary depending upon availability (date and time of travel). The more advanced notice you Can give, the better opportunity for a lower rate. Parking is also available near the station (NOT affiliated with Amtrak). Parking does fill up early (10a) due to construction of a new parking structure. Check online for additional parking options near the station. I suggested contacting Amtrak.com (800-USA-RAIL) and plan ahead for your trip.
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