Upon finishing each mission, you will face an emergency mission afterward. The order you tackle the standard missions doesn't matter, though we recommend choosing the harder ones first. For example, if you often die at the end of raptor attack, get it out of the way first. If you die on your first mission, you can just reset the game so it doesn't reduce your limited number of continues. There's also nothing worse than going through the trouble of playing a bunch of easy missions just to save the one you've never been able to do for the very end, and lose all your continues there. Choosing it first will make you more familiar with that mission and spare you some frustration when you lose.
The order doesn't really matter when you're starting out. Get familiar with each mission. It's more important to be able to finish them at all than to finish them in a certain order; once you can do that you can be fussy with the order. If there is a mission you haven't finished, always choose it first.
Our recommended order is Raptor Attack, Seek and Destroy, Blockade, High Ptera, Protect the Gallimimus, and T-Rex Carnage. This is only a rough recommendation, and a different order may be more suited to you. This order was chosen by considering the difficulty of the last segment of Raptor Attack (most of the level is cheese easy when you're used to it) and of Seek and Destroy, the chance of being killed by the boss in Blockade, the chance of falling off the cliff and dying in High Ptera, the chance of being killed by the helicopter in Protect the Gallimimus, and the chance of falling into the pit at the end of T-Rex Carnage. (Other than these things, the levels shouldn't be too hard with this walkthrough and a little practice.) Depending on how much difficulty you have with these, a different order may be more appropriate for you. For example, you might have practiced Raptor Attack a lot, while you always fall into the pit at the end of T-Rex Carnage; in that case, do T-Rex Carnage first.