The good thing is you should be level 4 or 5 by this time and can abandon the starter ship at level 10. You will get a choice of 3 different types of ships, Kirk's Constitution class cruiser, Oberth Science Vessel and Archer's "Akiraprise" Light Escort. There are 3 other ships to pick from but you'll have to pay money for them (and totally not worth the cost, so don't).
Here I have to correct you.
The NX Class, the Oberth and the original Constitution are all C-Store ships and can be bought at starter level. if he bought them he could replace the Miranda.
At level 10 you can choose between a Constitution Refit, a Nova class science ship or a Saber class escort for free.