I tried to play the game, and failed utterly.
I did the tutorial, then tried to make my way to new vegas. Of course, I ran into caesar's legion at that one town. I saved the people they kidnapped, unaware that it would mean that my character was going to be hunted by high-level enemies with powerful gear for the rest of the game. I did try to do the thing where you run to an NCR base and let them kill them, but the legion murdered the entire base they were so op. Despite this, I somehow managed to beat them (partially the NCR wore them down a bit, yeah, they didn't kill one legion guy despite their being a dozen of them…) I then tried to do that quest with ghouls that want to go into outer space. I tried to do one quest, and got owned by lizards that looked like the ones you fight during the tutorial, but apparently are far more powerful. I was also having a problem with my character not progressing at all as I leveled. Everything kept getting harder and harder to kill, despite the fact that I was in fact specializing in ONE combat skill. One of the last things I fought was a scorpion which appeared to be immune to all damage, even though I was using armor-piercing rounds. Those rounds also didn't do much to the legion guys. I think I expended all my ammo on them and had to melee them.
Anyway, after all this, I gave up, since I obviously completely screwed up my own game. And I was playing on the default difficulty mind you.
Now I'm thinking of trying again, but obviously I need to ask what you're actually supposed to do in this game, since questing when you're low level is obviously a VERY bad idea (someone else I talked to referred to that legion quest I did as a 'noob trap').
Best Answer
Unlike FO3 and 4, the game has very few level scaling enemies - most areas have the same enemies whether you fight them at level 1 or level 30. If you run into an enemy or group of enemies you can't deal with, it is somewhat assumed you'll run away and come back later (experienced players may use specific items and tricks to defeat or sneak around them).
Something else to keep in mind is that many of the quests in the game, including the one mentioned in the OP, have non-violent solutions. I won't spoil it for you on that quest, but if you want to know what options you have besides fighting the Legion you can always look up the quest online.
With all that said, the beginning of the game can definitely feel tough, since it's easy to go a little way in the wrong direction and run into an enemy that is too difficult for you to defeat. In general you can try to stick to the main quest until you reach New Vegas, if you want - the locations it sends you to will all be low level, and I believe all of the quests can be completed without fighting. On the other hand, most of the side quests you are given should be intended for low level players, so if you are running into enemies that are too difficult, check your map and see if there are alternative routes to the quest location.