If you are talking about FLV videos I think they dont bypass Firefox cache, they are stored in it, not in Flash internal secret hidden cache... I dont think what you are seeing in Process Monitor is the actual flv file being cache but maybe something else flash related, just guessing but maybe if you blocked local settings from being stored, maybe what you are seeing is the flash code trying to store the settings and the flash plugin refusing over and over...
You can use this Firefox extension to control Firefox caching mechanism: BetterCache.
The description emphasizes its capabilities to make everything cache despite of http headers and the like but actually it incorporates a whitelist/blacklist feature that should let you put a rule to never cache flv files (never tried it myself though).
Anyway I think what you are experiencing is not related to disk caching slowing down flash playing but something else, unless there is a bug in firefox flash plugin or something is wrong with your disk.

I would also recommend Mandriva over Ubuntu but any of them would be ok.
Whatever you choose I would advise to research if your network connection hardware is well supported under the distribution you will install. So even if you have troubles with other hardware you can be sure that you have connectivity to download drivers, package updates or just simply ask for help on the net.

Regarding PowerMarks, I tried it and at first sight I see three big limitations with it:

 - When importing from Firefox, if you have several profiles, it chooses just one, without letting you import the other profiles' bookmarks.
 - All imported bookmarks end up in the tree root. A choice to select where do you want the imported bookmarks to be put would be nice.
 - I didnt find any way to reorganize folders: drag and drop doesnt work in the folder tree frame, and only bookmark items show up in the right frame.