There are pre-painted non-collectible plastic minis from Reaper in their Legendary Encounters line. Those, D&D Minis, and the upcoming Paizo/Wizkids minis are the most on point.
We also use Dreamblade, Horroclix, and other minis of that sort from WotC and WizKids - our group demands lots of minis and none of us have the time for painting and that kind of stuff. Most of those are out of print though, and might be classified as games as well. The bases are wildly inappropriate, usually taking up Large space at a minimum, but we get by.
For big lots, I mainly resort to eBay. Not sure if customs will look at them differently if sold used from a random dude or not.