Pay-to-not-wait, pay-to-progress-faster, pay-to-look-fucking-badass.
As much as I like telling people to spend a few bucks to support the game, I would advise against spend money before you even try the game.
Every new account starts you off with free 50 platinum and many weapon and warframe slots. While you can buy platinum packs so you can spend them on getting even more slots, you can actually roll platinum discounts as a login reward, and you can simply use that to get a substantial discount to get platinum instead.
Warframe ultimately is a loot-grind game, and the more weapons & warframes you leveled, the higher the level you will become as a player (the game labelled as "Mastery Rank").
The real money sink is usually tie to cosmetics, and that is what the vets spend their money on.