For your multiplayer problem hamachi wouldn't do anything at all unless you are playing with a friend who is also using it and hosting the server... just sort the servers by ping and choose the lowest one. If the pings are still too high then someone in your house (or you) is probably downloading something.
I recommend playing the heck out of native Warband before trying the multiplayer and other mods because both of those tend to be more difficult.
As for mods:
Singleplayer:
Brytenwalda (mid-600s British Isles), Sword of Damocles: Warlords, Floris Mod Pack, Prophesy of Pendor, and 1257 AD are all excellent mods and there are many others.
Mutliplayer:
Mount&Musket is a Napoleonic warfare mod, with regular weekly events for both Europe and North America.
Mount&Gladius is a recently revived Roman mod and currently has Romans vs Gauls although it is still in heavy development.
Secession is a US Civil War mod that is pretty neat although still needs more development. It also has a weekly event.
Vikingr is another excellent mod, although unfortunately it doesn't have any NA servers.
There are also various other mods listed here:
http://forums.taleworlds.com/index.php/board,165.0.html
EDIT: I do NOT recommend the Persistent World mods, most of the servers have pages of rules (which are hardly followed but still bannable), and a particularly whiny and trollish community with lots of griefers.