I will try to answer both of your questions. Regarding the first one, it majorly depends on your personal liking, but I will do my best to propose some suggestions built on personal experience.
First of all, install FOSE http://fose.silverlock.org/ and ArchiveInvalidation Invalidated plus Fallout Mod Manager if you haven't already done that.
There are 3 amazing quest mods created by PuceMoose which make those vanilla ones ...inferior at best.
http://fallout3nexus.com/downloads/file.php?id=4730
http://fallout3nexus.com/downloads/file.php?id=5630
http://fallout3nexus.com/downloads/file.php?id=6921
I see you mentioned Arwen's Tweaks but I will recommend another overhaul mod called Fallout's Wanderer's Edition with fantastic incorporated quality mods (including Arwen mods).
http://fallout3nexus.com/downloads/file.php?id=2761
I also strongly recommend installing DarnifiedUI mod which greatly enhances User Interface of the game. You can find it here on gamesas Forums in Fallout 3 modding board.
There are of course many other great mods for you to consider: MMM (new creatures mod by Martigen), XFO (some modules of it are included in FWE), EVE, CRAFT, CALIBR, Fellout, Owned, Closer To Classics (amazing bunch of mods, incompatibile with DarnUI), more perks by dree74. Look 'em up on www.fallout3nexus.com website.
As of question number two, all you have to do is backup data folder and have it copied over previously installed (on the new machine) patched vanilla version of the game