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.
Oops, my bad. I mis-read the wiki page. But yeah the ship types still apply, Constitution Refit == Cruiser, Nova == Science Vessel, Saber == Escort.
I've never gotten the hang of steering with the mouse. WASD all the way, bro!
Its not exactly WASD vs mouse piloting. Each has their advantages so the key is knowing when to use the keyboard and when to use the mouse.
Typically, I prefer to pilot with the mouse by pressing both mouse buttons down. The advantage is that the camera is turning with your ship so its a simple point and aim system. It is great for out of combat movement.
Using WASD doesn't turn your camera and as a result I find that it is difficult to point the ship in the right direction. Having said that, I use WASD a lot during ship combat to make minor tweaks to my ship's orientation and speed to keep weapons pointed at a moving target, especially when I'm flying in reverse.