New Vegas engages in a bit of de facto railroading at the beginning, and I don't think anyone will disagree with you that the In Media Res opening felt a bit unfocused or that it was a bad move having Doc Mitchell decide to hand you his vault suit and his invaluable, irreplaceable personal computer as parting gifts. F3's beginning, for its own flaws, was much more dynamic and self-contained and really felt like it was thrusting you out into the wasteland. That's really more design than writing, though, and from the moment Doc Mitchell opened his mouth (in fact, from the moment Benny starts speaking in the opening cutscene) New Vegas's writing was leaps and bounds ahead of 3's in characterization, believability, and depth. As to that railroading, they might keep you to the south of the map to start with but they give you plenty to explore down there, and it's not like it takes you any real time at all to get around those mountains. On top of that, once you've got a playthrough's worth of experience under your belt, you've got half a dozen viable ways to circumvent the meatwalls herding you towards Primm and skip straight to Novac, or even Vegas. My own brother decided that was where the action was and went straight there from Goodsprings on his first playthrough, which isn't by any means unprecedented amongst seasoned Fallout 3 veterans.
To be honest, I greatly prefer New Vegas' opening, as it's in line with Fallout and Fallout 2. You're given an objective and sent on your merry way. The games consciously avoided giving the player character any particular background or motivation, specifically so that the player can write their own on the tabula rasa provided. You can start defining your character as early as the first town in Fallout or the first interactions in Fallout 2.
I know I hated Fallout 3's extended intro, as rather than creating my own character as Fallout always permitted me to (FOBOS doesn't count), I was given someone else's creation to use. The fundamental character elements were already defined and all I could was fill in the blanks. I could not deviate from the archetype of loving child in search of Daddy. The token option to tell Dad to fuck off was just that: Token. The game would freeze the storyline until I decided to be a good child and work with Daddy.
Compare that to New Vegas, where if you don't like someone you can skip or work around them. In Fallout 2, you could easily avoid taking a side in the game-defining conflict for NorCal and simply focus on helping your village. To be honest, Fallout 2 would have been much better without the whole Enclave subplot, instead focusing on what really mattered, such as the aforementioned conflict. I won't even mention Fallout, where you can tackle the storyline in any order, up to and including killing the supermutants without finding the waterchip (though that's not fully supported by the game).
As to believability, I can see how some might think The Courier's motivation was lacking compared to the Lone Wanderer's, but even if you're not out for blood (my Courier certainly wasn't) your motivation should be absolutely clear: "I am a courier. I was paid to make a delivery. I have a slip here detailing that delivery, and the fact that I am a courier. Failing to make this delivery will probably have consequences, the very least of which will be an irrecoverable impact to my professional credibility. I should probably recover the chip and finish the job, and I know where the man who took it is headed." Chasing down this macguffin leads you into the convergence of intrigues that is Vegas, where, by association and blind chance, you're caught up in things and eventually end up taking your chance to give the people of New Vegas (your de facto home) what you think is the best future for them, or to make a grab for what you think is best for you. If you feel this is a bit high-flung, deliver the chip to House like a good courier doing a job and then do what merc work you please and ignore the main quest in order to freely explore the wasteland, as you said you wanted to in the first place.
In New Vegas, the motivations of the player character are up to the player to establish. The developers purposefully did not establish them beyond very broad strokes, because it was designed as a role playing game, where the gamer creates the character and lays down what drives him or her to do the things they do. The game gives plenty of opportunity for expressing the character and defining them as well, including dozens of dialogue options that are placed for the sake of roleplaying and give different reactions from NPCs.
Generally, I find the complaint that the developers did not create the motivations for the player bizarre. It's a role playing game, what did you expect?
Your community's reputation as a warm, welcoming place where people can have discussions about a franchise they enjoy is well known across the internet, and clearly well founded given the helpful, insightful comment you have provided. Truly, I am moved both by your eloquence and the extent to which you were willing to analyse my concerns on a point-for-point basis and offer your own thoughts as to why they did or did not apply as appropriate.
Yamu already explained the standing policy well. As an administrator, I'd like to add that I've asked Akratus to refrain from ad hominem arguments, especially in a thread warranting discussion.