If you want then you can fly all story missions back-to-back, without freelancing, trading, pirating or looting wrecks between missions. You just have to have the right amount of the right commodity in your hold at the end of a story mission or (in some cases) simply know what to
buy in order to level up.
Knowing these tricks can be useful if you want to beat the game with a certain ship (say, the Starflier) without wasting time on non-story missions. This way you don't have to do any extra-curricular activities unless you want to. Have a look at the thread
Level 7 in the Spoiler Forum for specific tips.
Note: if you want to go through the game in the shortest time possible then funds won't be ample and you won't have access to the best weapons because getting them requires extra time and money; also, the choice of ships is restricted to those that have sufficient cargo space (Piranha/Barracuda instead of Cavalier/Drake).