Big topic! Here we go!
Legion or NCR? NCR is like the good guys/ military. Legion is a brutal group of people who play the "bad guys" role. It's up to you but I prefer playing good.
Brotherhood of Steel: As far as I know, they're independent but in the neutral to good area. They can be at odds with NCR on some things but again, it's up to you. I feel like they're even more at odds with legion but I haven't joined them as I can't get into FO:NV like I did Fallout 3. In Fallout 3, the Brotherhood was the good force.
Up to this point: You were shot in the head while delivering some platinum chip. The courier who was originally tasked with the job quit and wanted you to have it for some unknown reason. You meet this guy in the DLC "Lonesome Road". Your sole plan was to chase down the man who shot you "Benny". You decide what to do with him when you find him. Upon reaching Vegas, Victor - the robot (owned by Mr. House) - tells you that Mr. House wants to meet you. You go to him and he proposes a deal with you. He wants the platinum chip because it can make his securitron robots even MORE deadly and he can control the strip. *YOU ARE HERE-ish*
Quests:
"The House Always Wins" I and II are Mr. House main story. "Render unto Caesar" is a Legion main quest. With Legion and NCR main quests, they will make each faction like or dislike you depending on who you're working for. "Wild Card" I'm not sure but search Google for "The Fallout Wiki". It has EVERYTHING about the game.
Stuff: There are sooo many places to get meds, I can't list them all. Goodsprings: Doc Mitch & general store; Novac: The doctor lady who "needs sterile medical supplies" lol. So on... Exploring will help too. The gunrunners are outside Vegas - just to the South of the East Freeside gate. They have the all-time best weapons. (Maybe armor? I forget)
Followers, the first follower that most people get is in Novac. Go into and up then out (you're now in the mouth) of the dinosaur. At night, there's a sniper named Boone. He'll give you a quest and once done, can become your follower. In Primm, there's a robot in the Mojave Express office (has a big sign on the building but it's the last building on the right as you enter from the bridge). If you have a high enough repair/ science skill, you can repair him and he'll be your follower as well. You can have up to one human follower and one non-human at the same time. Thus, Boone and ED-E (the robot) are typically the first two.
If you need to, start over and just explore around more and take the game slower. Go into caves instead of barreling through the main quest. Alternatively you could just go back to previous areas and explore. This will get you experience (helping your skills) and loot (getting your better weapons, armor, and meds).
Whew! That was a lot but I hope that helps!! :) Enjoy!
p.s. If you fast-travel less, the game won't be so rushed and it will give you more time to think through what's happening. I gave up fast-traveling all together back in The Elder Scrolls IV: Oblivion and Fallout 3. I enjoy Fallout and Elder Scrolls games much more now.