What kind of hardware do I need for a multi-person editing team?
The first thing is to separate your source assets from your projects.  Source assets are the biggest things and should never change.  They are generally best placed on a NAS RAID array on gigabit Ethernet or better (10G+ fiber links are nice if you can afford them, but not strictly needed).  Each editor can then pull down whatever source files they need locally (or possibly just work off the NAS, though I'd recommend local pull down).

Project files on the other hand could use things like versioning and locking to prevent conflicts from forming.  Project files change frequently since they store the actual editing decisions, but they are also much, much smaller than the static source files.  Personally, I back these up in a portion of the same directory structure on my external, but I don't have to worry about version control since I am not in a multi-user environment.

Any decent editor should be able to reasonably easily deal with wiring up to assets via relative paths and should be able to adjust for moving the project files around provided that similar directory structures are used on each editing system.

I personally organize with a folder per project with a source folder and a project folder and a swap folder in each, though that can be switched around to have a source folder and a projects folder with sub-folders for each project within it if you prefer that organization.

I know there are also more dedicated asset management systems out there, but I have never had need of playing with them beyond some light work with Adobe Vue which I don't think is still actively maintained and wasn't really designed for handling video as I understand it.