However in this case, time dilation due to speed will be present so the net effect will be that the clocks on the spacecraft will be slower than that on earth.

Escape velocity from earth is 11.186 km/s. Lets be generous and say the space ship can go 10x that. Using the calculations from the website below, time dilatation factor would be 1.0000000696110642 times slower. If i calculate correctly, you lose 2 point something seconds a year

After launch on Saturn V SA-504 on July 16, 1969 from pad 39A of Kennedy Space Center, Apollo 11 entered Earth orbit. After 1 1/2 Earth orbits, the S-IVB stage was re-ignited at 16:16:16 UT for a translunar injection burn of 5 minutes, 48 seconds putting the spacecraft on course for the moon. The CSM separated from the S-IVB stage containing the LM33 minutes later, turned around and docked with the LM at 16:56:03 UT. About an hour and 15 minutes later the S-IVB stage was injected into heliocentric orbit. During translunar coast a color TV transmission was made from Apollo 11 and on July 17 a 3-second mid-course correction burn of the main engine was performed. Lunar orbit insertion was achieved on July 19 at 17:21:50 UT by a retrograde firing of the main engine for 357.5 seconds while the spacecraft was behind the moon and out of contact with Earth. A later 17 second burn circularized the orbit. On July 20 Armstrong and Aldrin entered the LM for final checkout. At 18:11:53 the LM and CSM separated. After a visual inspection by Collins, the LM descent engine fired for 30 seconds at 19:08 UT, putting the craft into a descent orbit with a closest approach 14.5 km above the moon's surface. At 20:05 the LM descent engine fired for 756.3 seconds and descent to the lunar surface began

The time in empty space travels faster than time on Earth due to Earth causing a curve in spacetime

Its like this the curve means more space for something to travel across ie time where as a smooth spacetime takes less space for something to travel across like someone running across a valley while another runs across a flat surface.
Traveling faster is like running faster than someone else you will get to the finish line before them ie travel faster in space youll be in the future before the time you would if you went slower.

If you have good background credentials, especially in writing/journalism, it doesn't hurt to try. Apply with National Geographic or Lonely Planet. They're both good companies.