This game is a nightmare to understand for newer players. Some of us are lucky enough to be here when started the mod system and have had the luxury of learning each new part slowly over the last 3 years (?). You don't have that luxury.
You need to be MR3 to join a syndicate, and you pick them from the console on the left of your Liset (spaceship). You need to initiate (do all of them to get the starter sigils), then do missions with those sigils displayed on your warframe (appearance / regalia).
As you gain more points you get to rank up with sacrifices which can be quite expensive for newer players.
The syndicates either ally, like, neutral or hate one another, so you need to balance the work you do for them. Fastest way is to work for a couple of allied syndicates . Slower but bigger rewards for spreading it out between 4.
Lots more info here: http://warframe.wikia.com ... /wiki/Syndicates
Auras come from Alerts. Keep an eye open for them, clan mates will help you get them. you can also trade for them.
Progression is how you want it. Personally I completed the star map before 'wanting' anything. I had resources and 'farmed' very little to build what i could. Beat the boss to open the next area.
Archwing pretty optional right now. Worry about it later.