First playthrough? That's going back a while but probably selling Arcade into slavery. I would have loved to fight along side Moreno, tooting our gatling lasers, cutting swaths in the NCR ranks, leaving a trail of untold destruction and suffering in our wake...
Then again, I couldn't have saved Caesar (didn't have the medical know how) so I don't think I had much of a choice. Arcade was a good friend, but I was working on the assumption that Lanius would be crowned Caesar... not really what I had in mind for the future of the Legion. My understanding of Lanius at the time wasn't great, in fairness, and what I DID know was largely based on myth. Difficult choice to make for a first run. In retrospect, I personally do not see ANY future in the Legion even with Caesar (the Edwad one) at the helm.
Apart from that (and some minor slip-ups), I think my excitement actually did me a disservice. I just wanted to see everything and so quickly, so didn't really fully appreciate all the game had to offer. My initial perception of the game was a bit jaded, mostly by virtue of the way I approached it. I treated it like a typical Bethesda game and, to me, that's not what New Vegas is about. I still enjoyed it, of course, but you really need to experience all the paths you can take. I wouldn't advise a first-timer to follow the Legion path like I did; there really is a disproportionate amount of quests in favour of the NCR (NV's biggest flaw, IMO) and by siding with the Legion you're really shut out. I guess that comes down to time constraints.... damn pushy publishers!!
Don't take this the wrong way, but I don't understand regrets over eliminating the BoS if you're siding with House. There is simply no way you could reconcile the two. I suppose Veronica is a sweety, though, and my House character never met her, so perhaps you have to see it from that perspective, too