Install MediaWiki Yourself
If you are looking for an easy way to install a wiki check out Turnkey Linux's MediaWiki Appliance which is dead simple to install on any old piece of x86 hardware you have lying around. Pop in the CD, hit enter, it wipes your drive and you have a working system. (Although you still will need to do some customizations and write your own backup scripts etc). To restrict access see: http://www.mediawiki.org/wiki/Manual:Preventing_access
MediaWiki In A Box
If you want an out-of-the-box solution, hardware included, for only $599 you can buy an open source Wiki In A Box system all pre-configured with auto-backup and plugins to help with access control from a company my friend and I run, InnoBox Devices.
Alternatively, if you are looking for generic setup where users you select can make edits to documents but not lose the editing history, perhaps you should be looking into a version control system. You can pay a monthly fee ($25) on GitHub to have private git repositories and allow your friends to edit those repositories. (No server installation required!) The advantage of using git is that it will apply version control to anything, be it code, a microsoft word document, or an image. git + GitHub also has good access control through their "organizations" feature which makes it easy to add or remove users. The disadvantage is that git (and version control generally) has a steeper learning curve then most wikis. Additionally, git and GitHub are structured around repositories (collections of files) as opposed to single files. This may be fine if you can group your documents into projects of some sorts, but if you really are looking to build a searchable knowledge base of many different articles than a wiki would likely be more appropriate.