Like I said earlier, the only things you have to buy in game are Warframe and weapon slots. Like Idiotekque said, it's a really pretty game and has a really distinctive art style. The gunplay is well done, melee is actually pretty good once you get some stance mods that work with your weapon (combos get unlocked for individual weapon types).
The whole game relies upon Mods. Each Warframe has 4 unique abilities, Frost is cold based with balanced attacks & defensive powers, Nyx can cause enemies to fight each other or absorb all damage for a short time - then toss it back at the enemies surrounding her, Vauban can throw singularity grenades or electric turret-like grenades, Nova can open portals in the world allowing fast travel or toss a white-hot ball of antimatter that will decimate anything around it when it blows. Each frame is well thought out, and while some of the frames have what I call a 'throw-away' ability or two most allow some really interesting combinations with other players, as well as utility when you're soloing. Some of these Warframes are better at certain roles/missions than others, but all are useful on their own. (Note - all these ability mods are given to you when you build (or buy if you're rich/lazy) that Warframe. You don't have to rely on RNG to get these abilities.)
Then there are the universal Warframe mods. Individual mods cannot be bought from the cash shop, but they can be sold/bought from/to other players or picked up from fallen enemies (all enemies have their own drop tables). These mods do everything from raising your Warframe's shields or health, to allowing you to use your abilities at reduced energy cost, etc. There really are a lot of mods.. and while there are a few 'accepted top builds' for the different frames, you can experiment and see what works best for you.
Then there are weapon mods - these can do things like allow rifle hold more ammo, shoot incendiary rounds, make melee attacks faster, etc.
All of these mods start out with a base stat, but can be raised using 'doubles' or universal upgrade mods called fusion cores.
This is all kept in check by a max limit of mods and values in all Warframes and weapons.
You do only have 1 character, but that is what's great about the game, wanna be a tank? Switch to Rhino or Valkyr, wanna be a caster? Switch to Volt or Nyx. All in all there are 20 base frames in the game.
If you're playing solo or exclusively with new player friends, you're going to play your first choice for a bit before you can go head-to-head with a planetary boss to get the individual components for a new Warframe. There is a branching order that the planets are unlocked at and the one you're going for may actually be a few planets away from where you start, but you can get everything for nothing.. well aside from time. The Warframe wiki is a very useful & constantly updated website to figure out what planets you should be unlocking to get the frames you want. I currently have 9 frames, with parts and blueprints to make 10 more (but my gf has claimed all the 'girl frames' for herself so I haven't bothered making them yet...but it's coming). You're not going to get all 3 components you need from fighting the boss 1 time, but you do get 1/3 random pieces each time you fight him. I've actually gotten pretty lucky so far and mostly only need to do a boss 5 times (3 times on the lowest and nearly 20 times on the worst [I just had really bad luck on that one]).
[I know in my previous post I said I had 15 frames, I counted and it's 9 complete and 10 that I could have if I just hit the build button in my foundry).
Alternately, if you don't mind playing with people you don't know, you can look for a group that is fighting a specific boss using the chat system. They can 'taxi' you to a boss even if you haven't unlocked all the mission nodes on the way. Most won't be too happy if you can't contribute anything to the fight at all, but most people I've dealt with have been pretty nice.
Oh, or you can just join a clan and they will help you do anything you need - including allowing you to clan researched weapons and Warframe blueprints.
Weapons - again, you buy the blueprints for in game currency that you get from drops/completing missions etc. Then you use the resources that you've accumulated the same way to build them. Again, I haven't spent a real-world dime on Warframes or Weapons.
The game also has rare weapons and Warframe variants (Called 'Primes' - nothing major, cosmetic differences on warframes, slightly better stats on weapons only) that can be acquired through 'void missions'(end game stuff) or purchased from other players using platinum. Platinum is actually fairly easy to come by once you've played a bit. You will get multiples of the same mods and newer players or people with money to burn will always be looking for the rarer ones. Once you've put some time into the game, you will be able to make platinum selling your mod multiples. (For example, when I started playing there was a mod called Redirection that was hard to come by. I now have a maxed rank redirection, as well as 80 more that I could probably get at least 50-60 platinum for if I tried. Prime components also sell really well.)
The game recently added the 'new player experience' which is a really nice intro for new players, and allows an expanded selection of weapons than they used to have. They've also introduced a new quest system (in addition to the usual planetary missions and bosses) that span a few missions. The first quest makes sure new players get what are considered 'essential mods'. These mods are inferior to the dropped versions, meaning they can't be ranked up as much, but they will make the game easier for new players to get into and complete missions faster than when I first started (first 2 planets were pretty brutal in difficulty without some of those mods).
Like I said earlier, the game's latest (Friday morning) patch broke a few things, but they put out 4 hot-fixes so far over the weekend, and are fixing things all the time. They're also listening to player feedback on the new UI (which is admittedly prettier than the old one, but less functional for power-users [too many clicks when doing tasks between missions compared to the older UI - changing weapons, building new gear etc]). My current recommendation is to give it a week to let them sort the bugs out before jumping in right now.
All in all, I think I've played Warframe more than just about any game I've ever played (including WoW). I only really duo with my gf, and we're still having fun with it. We've got our own clan, done all the clan research we care about, and played 600+ hours each for less than $10. It's the least expensive free-2-play game I can think of. The platinum option is there for those who have the cash, or don't have a lot of time.
OH! While the game is a co-op PVE game, they've added a PvP endgame component that players are free to ignore or jump into once they're ready. It actually looks pretty fun, with a 4 person team attacking and another team setting up a base's defenses and trying to stop them.
PS - Idiot, if you do continue playing, upgrade your starting frame with a orokin reactor as soon as you can - it will double your warframes max mod energy capacity. You can get these from the cash shop, but you can also get them from alerts (short-timed missions with better rewards than regular missions).