SHIELD is a military organization (first American, now multi-national I believe). Imagine them as a cross between the CIA and a more visible version of Special Forces commandos. Their main job, as you can imagine, is fighting the minions of supervillains. At one point back in the 60s/70s, they had a giant flying aircraft carrier, kind of like the one in Tailspin (if they have that in England). I'm sure there's much more to say, but I can't think of it.
As for your initiation into Heroclix, congratulations! The models, as you say, can often get up into GW-level coolness, but the painting on most is still nowhere near that good. Still, on uniques especially, the painting is a lot better than you'd expect from mass-produced inch-high models.
Your teams...I think you may be right, the first could be a little better. I'm not acquainted with all of the versions of the figures that your using, but Probability Control and a medic could easily put that team over the top. On the other hand, the Experienced Sabretooth is quite probably the best deal for the points, and definitely your best fighter. Spiderman is a hard figure to use, and I'm not sure I have him figured out myself yet, so I can't help you there.
And yes, all versions of Firelord could be described as "turbo charged nutters." His numbers and powers drop off very quickly, but that's not necessarily bad if you use him right--a medic can heal him pretty easily, since his defense drops so low.