Neither, it's the mob level. The fact that you can't relate your "level" to mob level is another opacity, but the planet unlock progression does more or less go with the frame/weapon level, kinda sorta. Mastery Rank is a side-issue, it's more to do with how much stuff you've levelled up (weapons, frames, etc.), plus some minimum competence with the tests. A few weapons are locked behind MR, but the highest lock (the Dragon Nikana, a space katana) is MR 8 which isn't too long to get to.
As starter weapons, level up the MK-1s to 30 and then get some "proper" weapons. The Braton is a good one to go for if you like auto weapons, Strun if you like shotties; the Orthos a good melee, secondary any really (Lex is pretty good). I would put potatoes (Orokin Reactors/Catalysts, they double mod capacity) in both your starter frame and these weapons, so you have some headroom for mods, the built-in headroom is a bit stingy; also you'll probably have the starter things for a wee while. I'd recommend spending a little bit on plat to begin with (tenner or so) if and when you get a plat discount with the login "gift". That way you can buy on the player market some of the essential frame and weapon mods I listed a few posts up.
The game is basically a rhythm of crafting, modding, player market and actually playing. You craft things, you level them for MR, see if you like using them. If you like using them, you lavish a potato and some forma on them (forma-ing requires restarting the level of the thing from 0). That way, you are always both ranking something up, and using the things you like for the more important/difficult missions.
Once you get over the "hump" of the middle planets (where the easy PUGs dry up and you start solo slogging a bit) the game gets very addictive as your modding efforts start to pay off and frames and weapons become really powerful; also as you start experimenting with more of the frames. I'd recommend you start doing the T1 Void missions with the keys you get as soon as possible - apart from anything else, the Void maps are beautiful, and have many secrets to explore (particularly the Exterminate ones, once you've exterminated, you can spend some time exploring for secrets, it's quite good fun). Also, once you start getting Prime parts and good mods dropping, you start to move into becoming self-sufficient (because you can sell those bits and pieces for plat - usually enough to get the odd 12/20p for a weapon or warframe slot, or a potato or forma now and then) and no longer needing to buy plat (unless you want instant gratification of course).