How to make the spaceship stop looking like Christmas

With Update 9 a new intro/tutorial based on the E3 Trailer was added to the game and the option to replay it.

To replay the Tutorial open your profile page in game by pressing the xp/credits/platinum bar and you will now see a Tutorial button.

I don't recall how many Warframe and weapon slots you start with (I've bought several expansions for each), but here's how you can check how many you have of each:

^{edited for update 10 UI overhaul}
In the upper right, pick the Arsenal button. Then pick the Inventory button (right above mods). By default you should now be looking at your Warframes; it will list each Warframe you have, its rank, how much it sells for (almost always 10k credits), and also any empty Warframe slots you have. If you look in the upper left of this display, the next button to the right of the Warframe selection is weapons. If you pick that all of your weapons will be listed, along with their ranks & sell values. As with Warframes, if you scroll to the end of this list it will tell you how many empty slots you have.

I think you start with 2 Warframe slots and 6(?) weapon slots.