After reading about each plug-in in detail on the Elder Scroll Pages site, it seems that most of them have a bug that sets the various items you can attain to the level in which you install and the items don't level up. Am I correct in understanding that this can be rectified only by uninstalling the plug-in, making a new save after the uninstall, then reinstalling? I'd like to begin play with the plug-in's as opposed to having to wait till I'm 21+ level to get the best possible versions. (I wasn't sure if this belonged in the technical section or not since it's not a hardware/patch issue.)

*I'm playing vanilla Oblivion on the Xbox 360 and don't have access to the unofficial patch

Yes, it is a very weird bug with .esp files in general, and one for which there's not too many details I'm afraid. Basically items in containers and hand placed actors have their loot set the moment the .esp file they come from is installed in your game. If they use leveled lists, they will use your character's level at that moment to determine their output. Esm files don't have this problem.

The problem is avoided if the actors from the mod come from a leveled creature list, since those are determined the moment you enter the cell they are placed into, and thus will have appropriate loot for your level. The problem is partially avoided for respawning containers, they will have their initial loot set at the moment you install the mod as well, but following visits to the cell they're in after the respawning time is up (usually 3 days) will have them give appropriate loot.